Spc manual

Statistical Process Control

(SPC)

ES e
ES VAUXHALL

STATISTICAL PROCESS

CONTROL
(SPC)
REFERENCE MANUAL
Ie 19 Sd 1055 ca

Fig 1992, © 1995
Chrysler Corporation, Ford Motor Company, and General Motors Corporation

Licensed under Copyright with Ford/Geaeral Motor Chrysler
Further Copies obtainable from:

Carwin Continuos Li Unit 1 Trade Link, Western Ave, West Thurrock, Gays, Essex, ENGLAND
‘Tel 44(01708) 861335: Fax 4401708) 867981

FOREWORD

‘This Reference Manual was prepared by the quality and supplie assessment stas at Chrysler, Ford and
General Motors, working under te auspices fthe Automotive Division ofthe American Society fr Quali
Control Supplier Quality Requirements Task Fore, in collaboration withthe Automotive Industry Action
Group.

‘The ASQCIALAG Task Force charter is to standardize the reference manuals, reporting formats end
technical nomenclature used by Chrysler Ford ad General Motors in thir respective supper assessment
systems Supplier Quality Assurance, Total Quality Excellence and Targets for Excellence According this
Reference Manual cn be used ty any suplir to develop information respondin to th requirements af
‘ther Chrysler's, Ford or General Motor’ suplier assessment systems

‘Until now, there has been no unid formal approach i the automotive industry on statisti process
control. Certain manufacturers provided methods or their suppliers, while hers bad no specie
requirements. In an lor o simplify and minimize varition in supplie quality requirements, Chrysler,
For, and General Motors agreed to develop and, through AIAG, distribute thie manual The work team
‘responsible forthe Manuals content was ed hy Leonard A Brown of General Motos.

‘The manual shouldbe considered an introduction to statistical proces contra, It isnot intended it
lation of statistical methods sulted to particular processes or commodities nor il intended 0 be
comprehensive of ll SPC techniques, Questions on the use of alternate methods shoud be referred to Your
customers quality activity.

‘The Task Fore gratefully acknowledges: the senior leadership and commitment of Vic Presents Thomas
1, Stallkamp at Chrysler, Clinton D, Lauer at For and Donald A. Pais at General Motors; the technical
competence and hard work of their quality and supplier assesement cans ani the invaluable costras
al the Automotive Industry Action Group (under AIAG Executive Director Joseph Te, Pela) In the
development, production and distribution 0 this Reference manual

‘We also wish to thank the ASQO reading team ld y Tripp Martin of Peterson Spring, wh reviewed the
Manual and inthe process made valuable contributions (Inte and content

Bruce W. Pince
‘Task Force Coordinator
Sandy Corporation
Troy, Michigan
December, 1001

‘This Mona is copyrighted by ALLA. all rights reserved, 1901, Additional copie can be ordered from
ALAS. andor permission to copy portions af the Manual fr use within super organeations may be
obtained rom ALLA. a (19) 896-9570

ACKNOWLEDGEMENT

‘The joint consensus onthe contents ofthis document was effected through Task Team Subcommittee
Monibers representing Genera Motor, Ford and Chrysler, respectively, whose approval signatures appear
below, and who grateflly acknowledge the sgiicant contribution of Pete Jessup of the Ford Motor
Company, who wis responsible or developing ho majority ofthe material found in Chapters 1, I, an I,
and the Appendix of ths document

larveyGolter ofthe Chrysler Corporation contributed concepts relative to proces capability and capa
ity studies, found in the introduction section of Chapter Jack Herman of Da Pont contributed some ofthe
concepts relative to capability and performance indices andthe importance of measurement variability,
found in portions of Chapters I and IV, respective,

‘The General Motors Powertrain Division contributed the discusion and examples relative to sugrouping
and process overadjustment. The section in Chapter I which provides understanding of proces capability
“nd elated sues was developed by the General Motors Corporate Statistical Review Comites, This
amie also contributed tothe development af Chapter IV, Process Measurement Systems Analysis, as
las to some Appendix items.

Finally, valuable input to all sections of the manual was provided by ASQC representatives Greg Grushka,
Doug Berg, and Tripp Mas

oad bam. Ua o Last fr Aland seu

“Leonard À Brown, GM. Victor W Lowe, Ford David R Benham, Chrysler

December 1901

Chapter

Chapter I

TABLE OF CONTENTS

EYTHODUCHON TO CONTINUAL IMPROVEMENT AND
STATISTICAL PROCESS CONTROL «10»

PREVENTION VERSUS DETECTION I. 5
A PROCESS CONTROL SYSTEM... E 1
VARIATION: COMMON AND SPECIAL CAUSES... 9
LOCAL ACTIONS AND ACTIONS ON THE SYSTEM. u
PROCESS CONTROL AND PROCESS CAPABILITY . 5

(THE PROCESS IMPROVEMENT CYCLE AND
PROCESS CONTROL..."

Section 7 CONTROL CHARTS: TOOLS FOR PROCESS CONTROL
Section 8 BENEFITS OF CONTROL CHARTS...

CONTROL CHART FOR VARIABLES .........- 2
Section 1 AVERAGE AND RANGE CHARTS (X AND R) . 2
A. GATHER DATA, . oa
B. CALCULATE CONTROL LIMITS Lu El
(©. INTERPRET FOR PROCESS CONTROL...
D. INTERPRET FOR PROCESS CAPABILITY ......... sr
Section 2 AVERAGE AND STANDARD DEVIATION CHARTS
ANDO ernennen see 68
A. GATHER DATA spires sein 65
B. CALCULATE CONTROL LIMITS e
©. INTERPRET FOR PROCESS CONTROL aa
D. INTERPRET FOR PROCESS CAPABILITY e
Section $ MEDIAN CHARTS (X ANDR) . 6
A. GATHER DATA A 8
B. CALCULATE CONTROL LIMITS. e
C. INTERPRET FOR PROCESS CONTROL... m
D. INTERPRET FOR PROCESS CAPABILITY a
E. ALTERNATE APPROACH TO MEDIAN CHART 2
Section 4 CHARTS FOR INDIVIDUALS AND MOVING RANGE &-MR). 75
A, GATHER DATA, 2
B. CALCULATE CONTROL LIMITS 6
©. INTERPRET FOR PROCESS CONTROL a
D. INTERPRET FOR PROCESS CAPABILITY n
Section 5 UNDERSTANDING PROCESS CAPABILITY AND PROCESS
PERFORMANCE FOR VARIABLES DATA es 79
A. DEFINITIONS OF PROCESS TERMS »
B. DEFINITION OF PROCESS MEASURES 80
(©. DESCRIPTION OF CONDITIONS AND ASSUMPTIONS E
D. SUGGESTED USE OF PROCESS MEASURES ss

Chapter HI CONTROL CHARTS FOR ATTRIBUTES

Chapter IV. PROCESS MEASUREMENT SYSTEMS ANALYSIS ..

TABLE OF CONTENTS - Continued

Section 1 THE p CHART FOR PROPORTION NONCONFORMING ..
A. GATHER DATA
B. CALCULATE CONTROL LIMITS.
©. INTERPRET THE CHART FOR PROCES
D. INTERPRET FOR PROCESS CAPABILITY
Section 2 THE np CHART FOR NUMBER NONCONFORMING .
A. GATHER DATA
B. CALCULATE CONTROL LIMTTS
©. INTERPRET FOR PROCESS CONTROL
D. INTERPRET FOR PROCESS CAPABILITY
Section 3 THE CHART FOR NUMBER OF NONCONFORMETIES
A. GATHER DATA
B. CALCULATE CONTROL LIMITS
(©. INTERPRET FOR PROCESS CONTROL
D. INTERPRET FOR PROCESS CAPABILITY
Section 4 THE u CHART FOR NONCONFORMITIES PER UNF
A. GATHER DATA
B. CALCULATE CONTROL LIMITS
©. INTERPRET FOR PROCESS CONTROL
D. INTERPRET FOR PROCESS CAPABILITY

'ONTROL.

Section 1 INTRODUCTION
Section 2 AVERAGE AND RANGE METHOD . .
A. CONDUCTING THE STUDY 5 m
B. CALCUIATIONS … m
(©. ANALYSIS OF RESULTS m
D. EXAMPLE ....... 7 ars

APPENDICES

„zonn u as»

SOME COMMENTS ON SURGROUPING .
OVERADJUSTMENT .

SELECTION PROCEDURE FOR THE USE OF THE CONTROL CHARTS
DESCRIBED IN THIS MANUAL.

RELATIONSHIP BETWEEN Com AND OTHER INDICES WITH
sep =r a

TABLE OF CONSTANTS AND FORMULAS FOR CONTROL CHARTS us
STANDARD NORMAL DISTRIBUTION ur
GLOSSARY OF TERMS AND SYMBOLS. se
REFERENCES AND SUGGESTED READINGS | 159
REPRODUCIBLE COPIES OF CONTROL CHART FORMS «| 161

m

19

10
n
12
5
u
5
16
”
1
19
20
a

2
25
25
E
»

seres

ses e

LIST OF ILLUSTRATIONS

Title Page
A Process Control System au en .6
Variation: Common and Special Causes ==. aval
Process Control and Procass Capability 2
‘The Process Improvement Cycle i 16
Control Charts im
Variables Data - Recut from Moss Intermediate or

Final Process Outoome +. 2
X and R Chart a 30
Y and R Chart Setup Data... es ®
X and R Chart = “Intl Study” se
X and R Chart With Control Limite 36
R Chart Point Beyond Control Limits 38
Chart ~ Runs (Range) s
Chart ~ Nonrandom Patterns. 2
X and R Chast - Control Limits Rcaleuation Rang) “
X Chart = Points Beyond Control Limits ....... resis 4B
X Chart Ram ..... E 2 4
X Chart - Nonsandom Patterns di 2.80

X and R Chart - Control Lits Recalculation
X and R Chart Extended Limits

Process Variation Relative To Specification Limits
Calling the Process Capability
Evaluating the Process Capabiliy

Data Colleton

X ands Chart

Median Control Chart x
Median Control Chart Interpretation
Individual and Moving Range Chart 2
Interpretation of Individuals and Moving Range Chart

Goal Pos” vs Loss Funcion &

Process Aliment to Requirements

Atnbute Data

1 Chart fr Proportion Noncenforming - Gathering Data

1 Chart for Proportion Nonconforming ~ Calculating Control Limits,

Sheet D. se
1 Chr for Proportion Nonconoring~ Cleat onto amis

‘Sheet 2 6
1 Chart or Proportion Nonconforming - Pont Beyond Conta Limit 98
1 Chan for Proportion Noncooforming — Runs ot 100

P Char for Proportion Noneonforming — Nonrandom Patterns m

LIST OF ILLUSTRATIONS - Continued.

Figure Title Page
a 1 Chart for Proportion Noncontorming — Control Limit Recaleuation .. 104
38 19 Chart for Number Nancontorming no
El + Chat for Number of Noncontormitios uz
40 1 Chart for Nonconformitics Per Unit 14
a Chart - Control Limits Reclewaton us
2 Gage Repetabiity and Reproducbliy Data Shot me
s Gage Repeatability and Reproducibility Report eee. 125
“ Gage Repeatability and Reproducibility Data Sheet - Example 128

ss (Gage Repeatability and Reproducbli Report = sample... 129

Chapter I
INTRODUCTION TO CONTINUAL
IMPROVEMENT AND STATISTICAL
PROCESS CONTROL

‘To prosper in today’s economic climate, we — automative manufacturers, suppliers and dealer organiza:
‘ions — must be dedicated o continua improvement. We must constantly sek more ficient ways to pros
(due product and series, These products and services must continue to improve 1 valu. We mst foes
‘upon our customers, both internal and external, and make customer satisfaction a primary business goal

‘To accomplish this, everyone in our organizations must be committed to improvement and tothe we of
(ifetive methods. bis manual address some ofthe needs in he second art. It eses several base
statistical methods which an be sed to make our eorts improvement more efactveDiflerent levels of
understanding are needed to perform different task, Tis manual a amed at praitioners end managers
‘begining the application of statistical methods. It wil al servo as reteset on these bese methods fr
those who are now using more advanced techniques. Not ll basic methods ar included her, Coverage of
other basic methods (such as checksheets, flowcharts, Pareto chart, cause an «fot diagrams) and some
Advanced methods (such as other control charts, designed experiment, Quality Function Deployment, ete)
available in Books and booklets such as thoe referenced in Appendir £.

‘The basic statistical methods uddresed in this book include hose associated with statistical process control
and process capability analysis. The fist chapter ofthis manual give some background of proces contro,
explain several important concepts such as special and common causes of variation, and intriiaces the
control chart which can bea very effective tol for analyzing and monitoring processes. The second ptes
describes the construction and us ofeontrl charts for variables daa (quintana data, or measurement)
X-barand R charts, X-barands charts, median chars, and X-MR Gndvidualand moving range hare, I
‘also describes the concept of process capability and discusses commonly used indies and ratios. The hid
Chapter describes several control charts for attributs data (qualitative data or counts): the p chet ap
(hart, chart and chart, The fourth chapter addresses the subject measurement systems analysis ad
presents an appropiate example. The Appendices include examples of subgrouing and overdjstonat a
low chart onthe use of control charts a table of constants and formulas, the standard normal distri,
and reproducible copies of bank char forms. A Glossary gives bit explanations of terms and symbols used
and the References section provides the reader with sources for Further study

Six points shouldbe made before the main discusion begins:

Fist, gthering data and sing statistical methods to interpret them arent endsin themes. The overall
im shouldbe increased understanding of the reader sproceses. Iti very easy become technique experts
without realizing any improvements neresed knowledge should become a basis oracion.

Second, the si conept of stdying variation and using statistical signals o improve performance canbe
applied to any are, Such areas can be onthe shop lor or he ae, Some examples are machines per.
‘formance characteristic), bookkeeping error rate) grosssales, trans esp rates) computer sy
tems (performance characteristics) and materials management (transit ümen) This manu focus upon
shop Noor applications ‘The readers encouraged to consul som ofthe references in Appendix Trad
state and service applications

oe e —___—_

PROCESS CONTROL

“Third SPC stands for statistical proces control It isunfortunte that in North America statistical methods
Areso oinaly applied to pars, raies han processes. Applicaton of statistical techniques o contol ont
put Guch as parts) shouldbe only the fs step. Until the processes which generate the output become the
Focus four efforts, hefull power ofthese methods to improve quality, increase productivity and educ cost
cannot be relied,

Fourth, although each pont i the texts ilusrated with a worked-out example, ral understanding af the
Slee involves deeper contact with proces control situations, The study of actual ase rom the readers
(Own job locaton or ram similar activities would ban important supplement to he text Theres however,
‘no substitute or hands~on experience with current proces information.

ith, tis manual shouldbe considered a first step toward theuseofstatstical methods. provides rules of
(ham whieh work in many instances, However, there exist exorptions where tx improper to blindly use
thee rules of amb. This manual doesnot epee the ned for practitioners increase thei knowledge ot
statistical methods and theory. Reuder are encouraged to pursue formal statistical education. Where the
der’ processes and application of atisical methods has advanced beyond the material covered here
therenderisalso encouraged to consult with persons who have Le proper knowledge and practice in stats
a theory as to the appropriateness af ober techies.

Sixth, measurement systems are critical to prope data analysis and they shouldbe well understood before
proces data ae collected, When such systems lack statistical control or thet aration accounts fora sub.
Santa portion of the total variation in process data, inappropriate decisions may be made, For the purposes
ofthismanualiewillbeassumed that ths ystom sundercontroland isnot asigaicaxt contributor to total
‘aration inthe data The reader referred tothe Measurement Systems Anais (MSA) Manual published
Uy the AIAG for more information on his opi.

Y EN >

THE NEED FOR PROCESS CONTROL

Detection — Tolerates Waste

Prevention — Avoids Waste

4. INTRODUCTION TO CONTINUAL IMPROVEMENT AND STATISTICAL PROCESS CONTROL
Section 1
PREVENTION VERSUS DETECTION

Inthe past, manufacturing often depended on production to make the product and on quality control to
spect the nal product and screen out tems nt meeting specications, In administrativo situations, work
often checked and rechecked in forts to th rrors Bath eases nvolve strategy of let, whichis

steil, eeaus allows time and materials to be invested in products or serre hat are nt aways us

ab.

Ris much more effective to vid waste by ot producing unusable output nthe ist place — a strategy of
recent

prevention strategy sounds sensible — even obvios — to most people is soil capturedin suchlogans
"Doit right the first tm.” However slogans re not enough, Whats required san understanding af
‘ements ofa statistical process contol system, The remaining seven subsections of this ntrdution over
these elements, and ean be viewed as answers ta the following questions

‘© What is meant bya process contro ystem? Section 2)

‘© How does variation affect process output? (Section 3)

+ How can statistical echniqustellwhethera problem local ia nature orinvolvesbroadersystems?
(Section)

‘© What is meant by a proces being statistical control? Whats meant by a proces being cape?
Sections)

‘© What is continual improvement cyl, and what part can process contol play in it Section 6)
(© Wat are contro chart, and how ae they used? (Section 7)
© What benefits can be expected from using control charts? Section 8)

‘As this material is being studied the reader may ich to er the Glossary in Appendix for rief defini
ions ot key terms and symbols

PROCESS CONTROL SYSTEM MODEL
WITH FEEDBACK

SES

Ep rour

THE WAY

oupwenr> | WE WORK/

uses» | BLENDING OF CUSTOMERS
memes») RESOURCES

cexmnonuenr |

e 2 A Le)
Ms ocre os
vor or cion

Figure 1. A Process Control System

INTRODUCTION TO CONTINUAL IMPROVEMENT AND STATISTICAL PROCESS CONTROL

Section 2
A PROCESS CONTROL SYSTEM

‘A process control system can be described as a feedback system. Statistical Process Control (SPC) is one
‘ype of feedback system. Other such systems, which are not statistical, also exist. Four element of hat
stem ar important to the disussions that vl follow:

1. The Process ~ By the proces, we mean the whole combination of suppliers, producers, people,
equipment, input materials methods and environment that work toptherto reduce out ad!
‘he customers who se that output (ee Figure D. The total performance ofthe proces depends
‘pon communication between supplier and customer, the way the proces i designe and ple,
‘ented, andon the way itis operated and managed. Te restof the process controleytem useful
‘only ft contributes either ta maintaninga level of excellence oto improving the total perfor
face ofthe proces.

2, Information About Performance — Much information about the actual performance ofthe
roots can be learned by studying the proces output. The most helpful information about the
Performance of process comes, however, for understanding the proces itself and sitema]
variability, Process characteristics (uch as temperatures, ue times, ed rates, absentecon,
{urmover, tardiness, or numberof interuptions) should be the ultimate focus of or frs. We
ed to determine the target values for hope characteristics which resul in the most productive
‘operation ofthe proces, and then monitor how near oo ar fom those Large values we ase Tt
‘his information gathered and interpreted correct, can show whether the process isacingin
inusual or unusual manner, Proper ations can then be takan, ina, correct the proves or.
the just-produced output When action is needed it must be timely and appropriate, or the infor:
‘malion-puhering effort is wasted

3. Action om the Process — Action onthe procss is frequently mast economical when taken to
‘ruven the important characteristics (process or output) from varying too far from thei target
values. This maintain thestabity nd Ue variation of the process cutput within acceptable i
its. Such ation might consis of changes inthe operations eg operator training. changes to the
incoming materials, et) or he more basic elements ofthe proves sel eth equipment =
‘which may need rehabilitation, how people communicate and relate ar deso ofthe proces es
a wbole — which may be vulnerable to changes in shop temperature or humidity). The eect of
actions shouldbe monitored, and farther analysis and ation shoul be taken i necessary.

4. Action onthe Output — Action onthe output frequently Iss economical when tis restricted
Lo deectingandorzeting out-at-specietion product without addresing the undering pro
‘ss problem. Unfortunately current output dors not consistently meet customer requirements,
‘ray be necessary to sor all products and toser or rework any nonconforming tems, This
must continue unt the necessary corrective cion on the process ha been taken and verd, oF
‘ntl the produc specifications have been changed

Its obvious hat inspection followed by action any onthe output s a poor substitute for effective process
management. Action only on he output shouldbe wed strely aan inter measure fo notable ra
le processes (see Section 3). Therefore, the discussions that Follow focas an gathering process information
and anyeing it so hat action can be taken o correct the proces isl.

Figure 2. Variation: Common and Special Causes

-8-

O ES

l INTRODUCTION TO CONTINUAL IMPROVEMENT AND STATISTICAL PROCESS CONTROL
Section 3
VARIATION: COMMON AND SPECIAL CAUSES

In order to effectively use process contra measurement dat, ts important to understand the concept of
variation, ar älesrued in Figure 2

No tuo products or characteristics are exact alike, because any process contains many sources of vara
ity The diferences among products may be large or they muy bo inmrasurably sal but they are always
‘present. The diameter ofa machined shat for isianc, would be susceptible potential variation rom the
machine (clearance, bearing wea, tool (strength, rate of wear), material ameter, hardness), operator
(part feed, accuracy of entering, maintenance Gubreation, replacement of worn part), nd environment
(temperature, constancy of power suppl). For another example, the Lime required to poctss un invoice
«ould vary according othe people performing various stes, the reliability of any equipment they were u
ing the aceoray and legibility ote invoice itself eh procedures allowed, nd the volume of other work
ETA

‘Some sources al variation in the proces cause short-term, ptce-to-piecediferences ~ eg, backlash and
learanceswithina machineanditfxturing, or th ocur aa bookkepers wore Other sourot of vars
ation tend to caus changes inthe output only over a longer period of tim, either gradual ca with ol or
‘machine wear, step-wise as with procedural changes, or regularly, swith envisoniental chang uch as
power surges. Therefore, the time period and condions over which measurements are made il flex the
mount ofthe total variation tat wl be present.

rom the standpoint of minimum requirement, the issveof variations often simplified: parts within sec
fication tolerance are acceptable, parts beyond speciation tolerances are not aceptable reports ont
are aceptable, ate reports are not acceptable However, to manage any process and reduce variation, the
‘aration must be traced back tot soures. The fist step sto make the distincion betwen common ad
Special uses of aration.

Wile individual measured valves may all be dierent as à group hey tend to fran a pattern that canbe
described asa distribution (se Figure 2). This distribution an be characterized ty:

© Location (typical value)
‘© Sprend (span of values fom small to largest)
‘Shape (the pattern of variation — whether iis symmetrical, owe, te)

{Common causes refer tothe many sources of variation within a process that has a stable and epratable
distribution over time, This sealed “in state of statistical contro,” in statistical Control, or sometimes
Just in contro.” Common causes behave like a stable syst of chance causes. If only common causes of
‘aration are present and donot change, the output ofa process s predictable

Special causes (often callo assignable cause) rfe to any factors casing variation that are not always act
ingon te proces. Thats, when they occur, they make the (vera process distribution change. Unies a
‘thespecial uses of variation are identified andacted pon, they will ont tae the proses otput in.
"unpredictable ways. If special causes of variation re present, the process outpt isnot stale over me,

‘The changes in the process distribution due to special causes can either be detrimental or beneficial. When
etrimental they need tobe identified and removed. When beneficial, they should be dened and made
permanent part ofthe proces, With some mature procesos (ie, processes which have undergone sever
‘les of continual improvement, the customer may give spec allowance o run a process wih a cost
tently ccuring special cause. Such allowances wil usual equis hat the proses contro! plans can assure
conformance to customer requirements and protect the process fom other special causes (See Seton D)

-9-

LOCAL ACTIONS AND ACTIONS ON THE SYSTEM

Local Actions

+ Are usually required to eliminate special causes of variation

+ Can usually be taken by people close to the process

+ Can correct typically about 15% of process problems
Actions on the System

+ Are usually required to reduce the variation due to common causes.
+ Almost always require management action for correction

+ Are needed to correct typically about 85% of process problems.

-10-

Section 4

LOCAL ACTIONS AND ACTIONS ON THE SYSTEM

‘Theres an important connection between the two types of variation just discussed and the type of action
necessary to reduce thes.

Simple statistical process control techniques can detect special causes of variation. Discovering special
‘use of variation and taking te proper ation is usally the responsibilty of someone wo dre soe
‘ected with he operation Although management mus sometimes be involved to correct the condon, the
‘solution ofa special ease of variation usually requires cal action This is special tru dug tar
roces improvement efforts As ne succes taking the proper action on speal uses, toe that Fe
‘ain vil often require management ation, rather than local ation,

‘These same simple statistical techniques can also indicate he extent of common causes of variation, ut the
«causes themselves need more detailed analysis to sat. Th coretion ofthese common causes alar
ation is usually the responsibility of management Sometines peopl directly connected with teopertion
will bein better position to ¡eat themand pass them onto management oracion Overall though the
solution of common causes of variation usual requires acia at he yer

Only relatively small proportion af excessive process var
= is orectabe local y people directly connected with the operation The mori {be other 83 ie
‘correctable only by management action on the stem. Confusion about the typeof action to tale ery
‘oily othe organization, in terms of wasted fr, delayed resolution of trouble, and aggravated problems,
ma be wrong. for example, to take lca action (eg, adjusting machine) when management action onthe
system is required eg selecting supplies that provide consisten! input material. Noveribalos, ne
‘amwork between management and those persons directly connected withthe operation oa mist Tor en.
ani reduction of common causes of process variation,

mn — industrial experience suggest about 16%

* Br. WB Deming has treated this issue in "What Happened in Japa?” Industrial Quality Contra).
‘Vol 24, No: , August, 1967, pages 89-80 andi other aries

** These observations were frst made by Dr. JM. Jura, and have been borne out in Dr. Deming expe-

one

-

o

Figure 2. Process Control and Process Capabiiy

ue

|. INTRODUCTION TO CONTINUAL IMPROVEMENT AND STATISTICAL PROCESS CONTROL
Section 5
PROCESS CONTROL AND PROCESS CAPABILITY

‘The goal af process control sytem isto make economically sound decisions about actions afeting the
process, This means balancing the consequences of taking action when atin sor necessary (overcontrol
or “tampering” versus filing to take action when ation is necessary Cndercontra) There iio must be
handled, however i the context ofthe two sources of variation previously mentioned special ets and
common causes (See Figure 3)

‘A process said be operating in statistical control when the only sources of variation ae from common
ass. One function ofa process control system, then, sto provide statistical signal when peral eases
‘variation are preset, and t avid giving alse signals when they ae not preset. This allows appropriate
action(s tobe taken spon those pera causes either removing them o, fthy are bene, making them
permanent),

‘When discussing process capability, o somewhat contrasting concepts need to be considered

‘+ Process capability is determined bythe variation that comes from common causes T generally rep-
resents the bes performance Le, minimum spread) ofthe proces sol as demonatroted when the
process being operated in asta of tata! control while the data are being collecte. respec,
‘ive of where the specifications may be with respect to the process location and/or spread

“+ Customers, however, internal or external are mor typically concerned with the overall output of
‘the process and how reltes to their requirements (defined as specifications, respective oe
proces variation,

Jn genera since proces in statistical control can be describo by a predictable distribution, the proportion
ofin-speoiiation pars canbe sit rom this distribution. A longasthe proces romaine
‘control and does not underg a change in location, spread or shape, wil contin to produce the sam
distribution of in-specification pars. The lst action on the proces should bet locate the process om the
target he proces spread is unacceptable, his strategy allows the minimum number of ot of pci
tion parts to be produced. Actions onthe system to reduce the variation from common cause are sally
rire to improve he ability ofthe process laits output to meet specications consisten). Pora mote
speciicunderstanding fo sujet a process capably, proces performance and ibeassumplions aso.
‘ted witht roer to Chapter I, Satin 5

Inshortthe process must este brought into statistical contra hy detecting and acting upon special cases
of variation. Then ts performance is predictable, and ls capable to meet customer expectations can be
seed. This à bss or continua improvement

Every process sujet to casiication based on capability and control. A process canbe ssl ato Lot
‘cases, a state by the fllowing chart

CONTROL.

MEETNO REQUIREMENTS comroL ORTHO.
ACCEPTABLE case cases |
NOT ACCEPTABLE case cases

1

oi <p

TATISTICAL PROCESS CONTROL

‘Section 5. Process Control and Process Caoablit (Cont)

‘Tobe aceptable, the process must bein a stat of statistical control and the inherent variation (capa)
must les than blueprint tolerance, The eal situation so Juve a Case 1 prooss where the process sin
ats control andthe ability to meet requirements aceptable. A Case 2 process isin contre but has
cesse common cause aration which must be reduced. A Case’ process mets requirement ecepably,
ut not in control special causes a variation must be identified and acted upon In Case the process
ot in contol nor acceptable; both common and special cause aration must be reduce.

Under orain ircumstance, the customer may allow a producer to runa process even thought isa Case3
Procns. These dreumstances muy includ:

+ The customers insensitive to variation within specication (See discusion on the oss function in
Chapter Il, Secon D.

+ ‘Teesconomics involved in aeting upon the special cause exo the Done toanyandalleastomers.
Economica allowable special causes may include ool weer, too egrind plc (exsona var

+ The special cause has been identified and hasbeen documented as consistent and predictable,
In thee situation, the following may be required bythe customer:

(© The proces is mature ie, the process has undergone several ele of continual improvement.

+ The special cause tobe allowed hasbeen shown tonct na consisten manner over nou periodo
tine

A process control plan iin effect which wil assure conformance to specification ofall proces out»
‘ut and protection from othe special cases ar inconsitony i the lowed special cause.

‘The aceotedpracticin tha automotive industry to calculate capability oly atra process has been dem
onstrated tobe na state af stalstia control. Capability sed a bass for prediction of how the process
‘ll perform using statistical data gathered from a process. Theres tle values making predictionsbased
ón data collected froma proces tht i ot stable and repeatable over time Special cases are responsible
For éhanges a the shape spread, ration fa process distribution, and thas rapidyinvaidate ni
Ay prediction, The vriou capability ndore and ratios are Dad, among oer things, onthe requirement
‘hak data used to ealulate them are gathered from press that are aa state of statistical control,

Capability indices can be divided into two categories: short-term and long-term. Short-term capability
“ties are based on measurements eallectd (rom one operating run. The data ae analyzed wit a control
‘hart for evidence hat the process is operating in sate statistical conte o speci uses re fund,
short arm capability inden can be lalate I the prowess oti ont, action regarding the special
‘uses of variation wil be required. This type of study Is often used to validate the ital parts produced
ftom a proces for customer submision. Another us, sometimes called a machine capability sty to.
late that a new or modified process actual performs within the engineering parameters

‘When process bas been found tobe stable and capabl of meeting requirements in the sort term, aie
tent kind of study is subsequently performed. Long-term capability studies const of measurements which
“recollected overa longer period etme. The data shouldbe collected for lon enough, ad in sucha wey,
Lo include al expected Sources of variation. Many of these sources of variation may not have bees observed
in the short-term study. Whenslcient data have been collected, the data are plotted on control chart,
“and if no special ase are found, lng ter capability and performance indices can de alculated.One use
Tor ths study i to describo te ability ofthe process ta satiny customer requirements overlong periods of
time with many possible sources of variation included = Le, o quantify process performance.

-u-

Section $. Process Gontral and Process Capabitty (Cont)

¡Several diferent indices have been developed because 1) no singe index can be universally applied to all
processes and 2) no given proces can be completely described by single index For example kreo
‘mended that ©, and Cy both be used (see Chapter, Seton 9), and further that they be combined with
sraphialtectiques (o better understand the relationship between the estimated distribution and the
Specification limits. a one sens, his amounts to comparing (and tying to aig) the “voice ofthe process
withthe “vice ofthe customer” (se also Reference 2,

‘Allindigas have weaknesses and can be misleading. Any inferences drawn from computed indices shou be
‘riven by appropriate interpretation ofthe data from which the indies were computed,

Automotive companies have et requirements or process capability. It isthe reader's esponsibility to om
musee wih ther customer and determine which indies to ue. In some case, it might be beat vo tse no
{ndexatallItsimportatto remember that mest capability indices include the produc speciation in the
formula Ifthe specification is inappropriate, or ot based upon customer requirements, much time ande:
fort may be wasted in trying to force the proces to conform. Section 5 of Chapter If deals with selected
«apabilty and performance indies and contains advice onthe application of howe Inden

-15-

ve

STAGES OF THE CONTINUAL PROCESS IMPROVEMENT CYCLE

1. ANALYZE THE PROCESS 2. MAINTAIN THE PROCESS
Les au eee
Écrits en
Bonen coo,

2. monove me PROCESS
oe

Figure 4. The Process improvement Cycle

16

Section 6

THE PROCESS IMPROVEMENT CYCLE AND PROCESS CONTROL

In applying the concept of contiual improvement to processes, there ea thre tage ele which canbe
sel (see Figure ) Every process sujet ta improvement can bo located somenhere In as le.

1. nae the Process

Abasic understanding f the procesisa must when considering roces improvement. Among the questions
Lo beanswered in order to achieve a better understanding ofthe proces are

‘© What should the proces be doing?

What can go wrong?
= What can vary inthis process?
= What do wo already know about this process variability?
= What parameters are most sensitive to variation?

© Wu he process doing?
= Is his proces producing scrap or output which requires rework?
= Does this process produce an output whichis in state of statistical contra
= Is the process capable?
= Is the proces reliable?

Many techniques maybe applied to gain better understanding ofthe process, such as group meetings, cone
station with people who develop or operate the process subject mater experts”, review oft proves!
stay or construction ofa Pailre Modes and Eitets Analysis (FMEA), Control chat explninsó in this
‘manual are powerful tols that shoud be used. Thes simple statistical methods help diferent betwen,
‘common and special uses of variation, The special eases of variation must be adresse: When sat ot
statistical control has been reached, capability index may be computed to sit in nsesing the proces
current level of long-term capahliy.

2. Maintain (Contr the Process

Once beter understanding of the process hasbeen achieved, the proces must be maintained at an appro-
pat evel of capability. Processes ar dynamic and wil change, The performance ofthe process pus be
‘monitored so fete measures to prevent undesirable change canbe taken, Desirable change sls must bo
‘understood and instittionaizel Again, the simple statistical methods explained inthis manual can sist
you. Construction and use ocoatralehars and other acs wallow for ficient mentoringol ihr process.
‘When the tool wed signals tha the roces has changed quick and efficent mearurescan be taken to slate
the causes() and at vpo them,

Ttistooeasy to stopat stag two inthe Cle. It isimportant to realize tat there ia ini o any company’s
resources. Some, perhaps many, processes should bo at this stage. However, ature to proced to the next
Sage inthis Ge con result in significant competitive dadvantage, The ttanment of sword lass re
«quires steady and planned effort to move into the next stage ofthe Process Improvement Cycle

-n-

Y E >

CESS CONTROL
Sections.

3. Improve the Process

Up to this pont th effort has ben to stabilize the processes and maintain them, However, for some proc.
‘ses, the customer willbe sensitive even to variation within engineering specications. In these instances
‘the value of continual improvement will not be realized unt variation reduced, At this pont additional
procs analysis eos, inluding moro advanced statistical methods such a desired experiments and ad-
‘ancod control charts may be useful Appendix H lists some helpful references for farther stay

(Cont)

roots improvement through variation reduction typically involves purposeful introducing changes into
he process and measuring he effects, The goals a better understanding the process, so that the common
nuse variation ean be further reduced. The ntent ofthis rection i improved quali at lower eos.

‘When new process parameters have been determined the Cycle shits hack to Analyre the races. Since

changes have been made, process stability will need Lobo reconfirmed. Tho proces then continues to move
‘round the Process Improvement Cycle

180

mes

-19-

vB

‘CONTROL CHARTS

Upper Control Limit

Center Line

Lower Control Limit

1. Collection:

ter data and plot on a chart.
2. Contra

+ Calelae tral control mis from process dat.

+ Leni special causes of variation and at upon them,
3. Analysis and Improvement

+ Quantify common cau variation; take action to reduce i

‘These three phases ao repeated for continual process improvement

Figure 5. Control Char

~~

O E

1. INTRODUCTION TO CONTINUAL IMPROVEMENT AND STATISTICAL PROCESS CONTROL,
Section 7
CONTROL CHARTS: TOOLS FOR PROCESS CONTROL

Dr. Walter Shewhart of the Bel Laboratorio, wile studying process datan the 19205, frst made the is
(üncion between controlled and uncontrolled variation, due to what we call common and special uses. He
developed simple but powerfl too toseparatethetwo ~ the contol chart. Since that im, coteolcharts|
ave Deen used suceshlly ina wide variety of proces contol stations, both in the U.S ad other toun.
tries, notably Japan. Experience hs shown that control charts efectiva drat attention toward special
‘uses of variation when they appear and ret Ihe extent of common cate variation that mus be reduced
Ey em or proces improvement.

Process improvement using contol charts i an itertive procedure, epeating the fundamental phases of
collection, control and analysis (se Figure 5). Fest data are guthered according toa plan Append A pro
vides input forsuchadata gathering plan) then, these data ar used calalate control nits, Vic arc
sis finterproting the data for statistical control when the proces sin statistical contol, Lean bet.
preted for process capability. To ee improvements control and capability, common nd special uses
variation must be identified and the process modiledaccordingy then Ihe cycle begins spi, as more
at ar gathered interpreted, and wel as the ass fraction.

1. Collection: Data for the characteristic (proces or output Deng sted are gathered and on
verted toa form that can heploted ona contralchart. These data ight be the measured value
dimension ofa machined piece, he number of an in ble of vis), ralla transit nes, ae
er of bookkeoping eros, et.

2. Control: Teal control limits are calculated based on the dat, They are drawn on the chart
guide to analyses. Control limits are ot specification limita or objectives, but are based On the
tural variability ofthe process and the sampling plan,

‘The data are then compared with the contol limits to ser whether the variation s stable and op
pear to come only fom common causes. IP special cases of aration are evident, the process
Studio to further determine what satin After ations (aly local) have been tke, fr.
ther data are colctd, control limits ae recalculated If necessary, and any additional specs)
‘utes are acted upon,

3. Analysis and Improvement: Afterall special causes have been addressed and the process is
‘unninginstatstia control, the control char continues as a monitoring tol Process apabiliy
an also be cleuated, Ith variation from common cassis excessive the process cannot pre
duce output that consistently meet customer requirements. The process cl must be vest
‘ated, and, typically, management action must be taken to improve the system,

Section 7.

(Cont)

en is found that although the process was aimed at the target value daring initial setup, the
actual process location (X) may ot match this value, For thase processes where the atl Ica-
ion deviates rom the target andthe ality to relate the process economical, consideration
Should be given to adjusting the process 0 hat better aligned with the arg® This assumes
that this adjustment doesnot affect the process variation. This may nat always hold true ut tho
causes for any possible increase in process variation flr e-Largeting the process shoul be une
‘derstood and assessed against both customer satsaction and economics,

‘The long-term performance ofthe procss must continue tobe analyzed, Thi is mast esl nc-
complished by a periodic and systematic reviow of the on-Boing contol charts. New evidence of
paca causes wll usally be revealed, Somo, when understod, willbe beneficial in reducing Use
‘verl process varity. Others, detrimental tothe process wi nod tobe understood and cor.
rected or removed

Por process which “in control” improvement fort wil often focas on reducing the common
aus variation nthe process. Reducing this aration will have the ect of shri” the cos
{eo limits onthe contol char—Le, the limits, pon thir recalculation, wil be cose together.
Many people, nt familiar wth control charts, el this is “penalizing” the process for improving.
‘They do not relie that fa roces is table and the contra limits aro eaeaated correct, he
‘hance thatthe proces wilerronoously yield out-of-control point isthe same regardless ofthe
istance between e control limits (ae alo Section).

(One are deserving mention sho question af recalculation of contol chat limits Once property
‘computed, and no changes to he common cons variation fte process occur, then conto!
limit remain legiimate Signal of special causes of variation do not reqirethercomputation of
control limits. Por long-term analysis of contol charts, iis bet to reaeulate conto] te a
Intrequenty as possible, but as dictated by the proces.

For continual process improvement, repeat thse three phases. Gather more data as appropriate; work to
ede process variation by operating the process in statistical control and, continue toanalyzo the process
variability

Bw

Y E >

BENEFITS OF CONTROL CHARTS

rol che

‘© Be used by operators for ongoing control of a process

‘© Help the process perform consistent, predictably, for quality and
cost

‘© Allow the process to achieve
= Higher qualty
= Lower unit cost
= Higher efecive capacity

+ Provide a common language for discussing the performance of the
process

+ Distinguish special from common causes of variation, as a guide to
local action or action on the system

OE et

Section 8
BENEFITS OF CONTROL CHARTS

‘The following lst summarizes some of the important benefits that can come from using control chars

© Control chart ar efectivo tools to understand process variation and help achieve statistical con
‘rol They often land themselves to being maintained a the job tation bythe operator. They give
‘the people clases othe operation reliable information on when action shold be taken — an on
wie action should at be taken (oz, oveadjustment ses Append D)

‘When process in statistical control ts performance sl be predictable Thus both producer and
customer can rely on consistent quality levels, and both can rely on sable cost of achlein that
‘ality level

© A process in statistical control can be farther improved through reduction of common causo va
ation and improved process centering argting). The expecte elects of proposed improvements
inthe sytem can be anticipated, and the actual eects of even relatively subtle changes cane iden
tied trough the control chart daa. The amount of data required vil vary with the process under
‘amination. Such process improvements may reduce cost and improve productivity by derresing
‘the variation around te arg al

® Control charts provide a common language for communicating information about the performance
‘ofa process — between the wo or three hifi that operate proces; betwen line production op.
erator, supervisor) and support activities (maintenance, materia contro, proces engineering,
‘quality control); betwen diferent stations i the process; between super and ser betwen the
‘manufeteing/assembly plant an the design engineering activi

+ Control charts, y distinguishing special rom common causes of variation, iv a good indication af
‘whether any problems ae likely tobe correctable locally or wil require management action Tis
‘minimizes the confusion, trutration, and excusive cost of misdirected prollnesahing ells

‘Theremainder ofthis manual describes techniques involved constructing and interpreting control char,
‘While reading these technical instructions and recommendations, itis wel 0 keep in mind to rn bens
‘hat can come ifthe control chart approach mastered and effectively used. For additional assistance el
{ive to which control chart shouldbe used for which situation, control chart selection diagram 6 provided
in Appendix C

NOTE: Two sample Bank control chart and proces log forms are shown in Appendix Lf charts

‘other than these are sed, the following minimum information should De on them: process
‘characteristic name; part number characteristic description measurement sero
Aor coded data; frequency of sample: sample sie; scale description e br, medion, ICH
‘scale values subgroup data, time, operator Initial or Hentai; gage or measurement
‘method used; a place to log process noes,

It might also be a god idea to include gage repeatability and reproducibility (GRARS)
information on each chart for added consideration in char interpretation and to zinfrce
‘he fet tht an anal of the measurement system has been performed

»-

CONTROL CHARTS RELATIVE TO THE PROCESS |

People | | Ensemen [ere
outcome is Messured
pil sezasse7e
+ Unit of Measure (mm.
Lo. 0e)
mais | | metoos + Origin (0 mm, 22 °F,
ee)
roces
‘Outcome Examples Control Char Examples
+ Shat OD, (inches) Bor Average of
Hole distance trom rterence suface (mm) the Measurement
À Grcui resistance (ohms).
À Rear wanst ime (noue) R Chan or Ranges
© Engineering change processing time (hours) ofthe Moasuremants

| ne measurement method must produce accurate and precise results overtime

Not Precise Precise

Not Accurate

de Ns

®

Accurater

Note: Some current metrology Iteraturo defines accuracy as Ihe Jack of bias

Figure 6. Variables Data - sui rom Measuring Intermediate or Final Process Outcome

= 26

a

Chapter II
CONTROL CHART FOR VARIABLES

Control charts for variables are powerful gos that can be used when measurements from a process are
available Examples would be the diameter ofa bearing, the closing effort ofa dor. o he time to review a

‘voucher, Variables charts — and especially thei most common forms, the X (x bar) and R charts repre
Sent the typical application of contra carting to proces control (See Figure 6)

Control Charts for variables are particularly useful for several reasons:

1, Most processes and their outputs have characerstis that are measurable o th potential app
ability broad.

2. A quanttuiv value (eg, “the diameter is 16.45 mm") contains more information than a simple
yesrno statement (eg, "ibe diameter is within speciation)

8. Although abtaining one piece of measured data generally more cosy than cbtaining one piecef
‘gofno-go ata fewer pices need to be checked to get more information about the proces son
Some eases tol measurement costs can be lower

44 Because fewer pies need tobe check before making reliable decisions, the time ap between
production of parts and corective action often can bo shortened,

‘5, With variables data, performance ofa proces ean be analyzed, and improvement can be quant:
Sedeven if all individual values are witin the specication Hts; thse important in seeking
ever ending improvement

Variables charts can explain process datain terms ofboth ts spend (iee-to-piee variability andits toc
"ion (process average). Because of his, contol charts for variable should always be prepared and analyte

in pars — one chart for ation and another for spread The most commonly used pair are the X and R

charts, X isthe average ofthe values in small subgroups — a measure o location; Ris the range of values
within ech subgroup (highest minus lowert)— a measure of spread

‘The X and R charts are discussed at length in Section ofthis chapter, Section 2 of this chapter treats X
ands charts (an alternative tothe R char, Section 3 teats media charts a simpler substiat or average
and range chart), and Section $f this chapter treats charts for individuals when decisions must be based
‘on single readings, not subgroup).

a

PREPARATION FOR USE OF CONTROL CHARTS

Establish an environment suitable for action
Define the process
Determine characteristics to be managed
Considerations:
= The customer's needs
= Current and potential problem areas.
Correlation between characteristics
Define the measurement system

Minimize unnecessary variation

-2

ll. CONTROL CHARTS FOR VARIABLES

Section 1
AVERAGE AND RANGE CHARTS (X AND R)

Before X and R charts ean be used, several proparatory steps must be taken:

+ Establish an environment suitable for action Any statistical method wil fil unless manage:
ment has prepared a responsible environment. Fear witha the organization tht inhibits people
from being candid must be removed. Management mut provide resources o yartiiptein audsap.
Dort improvement action.

+ Define the process, The process must be understood in terms ofits relationship to other opera
‘ons and users both upstream and downstream, and in terme ofthe process elements (people
‘equipment, material, methods und environment) that affect a each stage Techniques suche he
‘ause-and-effectdagram and the proces low diagram help make these relationships visible and
allow che pooling of experince from people who understand different aspcts of the proc

+ Determine characteristics to be charted. One example fa process designed to determine
‘hese characteristics is GM. Key Charatersstes Designation System (se Appendix, Reference
24) Study efforts shouldbe concentrated on those characteristics hat are mos promising or pr:
‘ss improvement an application ofthe Pareto principe). Several considerations aro appropriate.

= The customer neds: Tis includes both any subsequent processes that us the producto ser
{ce san input, and the final end-item customer, Communication ofthe needs of bth types of
Customer opi the proces where improvement on cures teamwork and under
Sanding

Current and potential problem areas: Consider existing evidence of waste or poor performance
(ee, strap, rework, extessivoovertine, mised targets nd areas of take. Upcoming changes
Hole design af the product or service, orto any element ofthe proces. These are opte
for improvement requiring application ofall he Alpine involved in running the business

= Comelation between characteristics: Por an efficient and effective study, take advantage fl
‘onships among characteristics, For instance the characteristic concern sical tones.
rete, volume), track correlated characters thats casieto measure log, weight) Als,
several nid characteristics onan item tend to vary together, e may besüficent o chart
‘only one ofthe, Warning: Statistical correlation doesnot necessary inply a cause and est
‘relationship beten variables. Inthe absence of existing procs knowledge, à designed opor.
‘ment may be needed 1 verify such relationships ond the significance

+ Define the measurement system. The characteristic must be operationally defined, 0 that
findings canbe communicated to al eoncarnedin ways that have the same meaning today as str.
‘ay. This involves spain what information tobe athered, where, how, and under st cond
tions The measurement equipment itself mus be predictable for both actaraey and prison =
period calibration is ot enough. Por more deta on this sac see Section IV, Tho definition ot
the characteristic will act thetype of control cart to be used — a variables data chart. suchas X
and R, or an attributes data chart as described in Seton Il,

© Minimize unnecessary variation. Unnecessary external causes of variation should be reduced
‘before the study beans. This could simply mean watching that the process 5 being operated
‘ade, or could mean conductingacontraled stay withinown input materials constant control
settings, ete Th purposes Lo avoid obvious problems tht could and shouldbe correct even wth
out use af control chars; this includes excessive process adjustment or overeotrol. nal eases, a
proces log should be kept notingall relevant events uch t tol changes, new row material ots,
{This wil ai in subsequent process analysts.

=D.

d 8 Chart

Figure 7.

so

O EN

4. CONTROL CHARTS FOR VARIABLES:
Secton 1. and A Chars (Cont)

A. GATHER DATA

‘An X andan chart, sa air, redeveloped from measurements of particular haructerstic ofthe proc
‘ss output. These data are reported in smal subgroups of costat sie, usual inching from 2 o 8 ron
Ssteutive pieces, wath subgroups taken periodically (ag, on every 15 minute, twice pr shi te). A data
‘Sathering plan must be developed and used as the bass for lin, recoding and plotting he data on a
hart

a

NOTE:

Select the Size, Frequency and Number of Subgroups (See Figure 7)

‘Subgroup Size — Te first key step in variables control charting he determination of ru

{Gora subgroups” — they wl determine tho effectiventss ad eliiency ofthe control chart.
that use them,

‘The subgroups shouldbe chosen so that opportunities for variation among the wits within
subgroup are snl I the variation within a subgroup represents the piece topics arab
ity over a very short period of time, then any nasal variation between subgroups wold
reflect changes inthe process that should be investigated for appropiate action,

Foranintial study ofa proces, the subgroups could typically consist of to 5 consecutively
produced piece representing only a single tool, head, de cv, ee. Ge, singe process
‘team, The intention is that the piees within each subgroup would al be produced under
very similar production conditions over avery short time interval wih no other systematic
Felationshipto eachother: hence variation within each group woul primar eect com>
mon causes. When these conditions are not met, the resulting control chart may nat eff:
‘rely discriminate special causes af variation ort may exhibit he unusual patterns notedin
paragraphs Cla and C.t of this Section, Sample sizes must romain constant or al sb
ous.

‘Subgroup Frequency — The goal sto dec changes inthe proces over time. Subgroups
shouldbe collected often enough, and at appropriate times, that they can reflect the potential
‘opportunities for change. Sach potential uses of change cold be due to workshiftdiffer-
fences or elo operators, warmup rend, tera lt, ee,

During aninitial proces study, the subgroups themselves are often taken consecutively oat
short intervals to detect whether the process can sit ta show other instability over rie
time periods As the proces demonstrates stability (or as process improvement ane mado)
{he time-period between subgroups can be inerensed,Suhgroup frequencies fr engoing po
‘Auction monitoring could be twice per shit hour, or seme other fsb rate

Number of Subgroups — The number of subgroups should satisfy two criteria. From a proce
‘essstandpoint, enough subgroups shouldbe gathered to assure that Ihe major sous tan
tion have had an opportunity to appear. General, 25 or more subgraups containing about
100 or more individual eatingsgivea good test for stability and, sable, good estimates of
{he proces Heaton and spread.

Ti some cases, existing data may be avilable which could accelerate tis first phase of the
study. However, they shouldbe used only if they are recent andi the basis forestal
groups clearly understad

For further understanding of the impact of subgrouping on control hart interpretation,
See Appendix.

-a-

AND R CONTROL CHART “INTIAL STUDY
ES [eax TE
x a oar ee
San) E TUTTO

DHBEEFE)

Figure 8. X and R Chart - Setup Da

»-

ll. CONTROL CHARTS FOR VARIABLES:
Section 1. Xand R Chars (Cont) - Gamer Data

An

As.

‘Set Up Control Charts and Record Raw Data See Figure 8)

X and R charts are normally drawa with the X chart above the R bart, and a data lock. The
values of X and Rwil be the vertical sales, while the sequence of subgroups through time willbe
the horizontal sal, The data values and the plot points for the range and average should be
aligned vertical.

"The data bloc should include space for each of the individual reading, I should alo include a
space or thesum of threading, the average the range andthe datetime or other Ment
ation of the subgroup.

Enter the individual values and the identification fr each sugrovp.
Calculate the Average (X) and Range (R) of Each Subgroup (See Figure 8)

‘The characteristics o bo ploted are the sample average (X) and the sample ange) foreach
subgroup collective, Itse ret the overall process average and it variability, respectively.

For each subgroup, caeuate:

ga kit Xe eut Xe

Ra ges = Kam

here the X, X. are individual values within the subgroup and asthe subgroup sample aie

XANO R CONTROL CHART - “INTIAL STUDY"
Ea Ex [TS
xx TT ET

=f | = DSB Y

Figure 9. X and R Chart = “ni Study"

sé

1. CONTROL CHARTS FOR VARIABLES
Section 1. X and A Charts (Cont) - Gather Data

Aa,

As.

Select Seales for the Control Charts (See Figure 9).

‘The vertical scale for the two chart are for measured value of X and Respectively. Some gen
rl peines or determining the seals muy be hp, although they may have tobe mii in
particular circumstances. For the X chart, the diffrence between the highest ond lowest values
bn the stale should bea lest 2 mes the dflereace between the highest and lowest of the su
‘troup averages (X). For the char, vales shoud extend from a lower value of zero to an upper
“alu about 2 Umes the largest range () encountered during ce inital period.

NOTE: One helpful guide sto set the sale spacing for the range chart tobe double that of
‘he average chart, 4 scle unit equal 1 inches on the averages chart, 1
sale unit would equal 02 inches on the range chart), For typical subgroup sizes, the
‘ontel nits for averages and ranges wil be about the same width visual id to
analysis

Plot the Averages and Ranges on the Control Charts (Soo Figure 9.

Plot the averages and anges on their respctivo chars, This shouldbe done a soon as posible
ter scaling has ben decided Connect te points with ines to help visualize pattems and ends

Brey san the plot paint ose i they look reasonable any point are substantially higher or
lower than the others, conv that the calculations and pots are correct. Make sur that the plot

Points forth corresponding X and Rare vertically in ine

NOTE: In order to renforo he practice ofall chart onthe production Noor having control
lit on them, initial run charts which da not yet have contol limit eaeaated (due
to invulcient amounts of data) shouldbe clearly Wentiied “uta Study”. Thus,
‘hee “nta Study" chart, wheter used for rt time capability o for studies
afer process improvements/changes, shoul be the only roces control charts
‘lowed onthe production Noor which donot have control Limits placed on them.

va

ac Dd a a
HE eee ele la
a] area

== a
az: aris mom == =a
==5==== TO Tao el
mm TE Tor En
mm si = = EAN se
a E Soars “
q E “us
TES 10MiNGO Y ONYX

Figure 10. X and Chart With Control mit

-00-

Bw

1. CONTROL CHARTS FOR VARIABLES.
Section 1. X and R Chars (Cont
8. CALCULATE CONTROL LIMITS
{Control limits forth ange chart are developed rt, chen those forthe char or averages. he calculations
{or the control limits fr variables chart use constants which appear as letters nto formulas that follow.
‘These actors, which fer according tothe subgroup size (a) are shown in bri ables accompanying the
respective formulas; more completo tables are shown in Appendix ES

B.1. Calculate the Average Range (R) and the Process Average (X) (See Figure 10)

For the study period, callate

B2. Caleulate the Control Limits (See Figure 10)
Control mits are calculated o show the extent hy which the subgroup averages and ranges would
‘vary fonly common causes of variation were present. They aro basedon the subgroup sample size
and the amount of witin-eubgroupvarnbilty reflected in the ranges. Calculo the upper and
Tower contol mia for ranges and for averages
UD

Lely = DR

eis AR
Lele R= AR

where Da sand A are constants varying by sample size, with valuesforsamplesizes from 21010
As shown in the following partial rable taken from Appendix E:

== E CIN CI ICI
aa Ziv | Boo] ae | 185] 180] 158
nl * III:
ne | 188 sl le 9] | #

(orsamplesizes below’, the LCL, woul technically bea negative number inthose cases there
0 lower control im is means hat fr a subgroup sizeof 6 sie “identical” measurement
Would not be unreasonable

B.S. Draw Lines for the Averages and the Control Limits on the Charts (See Figure 10)
Draw the average range (E and process average (X) as solid horizontal lines, the contro limits

(Clq, LC». UCLz, LCL) as dashed horizontal ines; abel the ines. During te tial study
hase hese are considered til control Hits,

--

PROGESS NOT IN CONTROL FOR RANGES
{POINTS BEYOND CONTROL LIMITS)

PROCESS IN CONTROL

FOR RANGES.

Dam)

FR EES CES le

Figure 11. R Chart - Point Beyond Control Limits

-8-

ll. CONTROL CHARTS FOR VARIABLES
‘Section 1. X and A Chars (Com

©. INTERPRET FOR PROCESS CONTROL

‘The control limits can be interpreted as follows: if the proces piee-to-piae variability and the process
average wereto remain constant at thei present level as estimated by R and X respectively, theindvid-
‘al subgroup ranges (Rand averages (X) woul vary by chance alone, but they woud seldom po beyond the
onto iit. Likewie, there would ben obvius trends or pattern nthe ata beyond wht would ely
‘occur dueto chance. The objective o control chart analysis teni) any evidence thatthe process vr
ly ar the process average ar not operating ata constant level that ono or both are au of statistical
control — and to take appropriate action Tha Rand X chas are snalyzed separatel, but comparison of
patterns between the to charts may sometimes give added insight nt special causes ft the proces,

©. Analyze the Data Plots on the Range Chart

‘Since the ability to interpret either the subgroup ranges or subgroupaverages depends on the est
‘mateofpiece-to-pics variability, the char analyzed re. The data pointe compared with
‘the control limits, for plats out of control or for ama) patterns or tends

2. Point Beyond the Control Limit (See Figure 11.) — The presence ofono ar more points he:
yond ether control mit is primary evidence of non-control at that pant. Since points be
Yond the contol limits would be very are only variation from common eases were pee
Sent, we presume that a special cause has accounted fr the extreme value. Therefore, any
point beyond e cotrl imi th signal or immediate analysis ofthe operation for these
Sal cause. Mark any data point that ar beyond the contro limits for urher investigation
‘and corrective action based on when tal special ease actually started. (See paragraph C2
ff tis section

point above the upper control mi for range generally a sgn of one or more ofthe foe
towing

{The contro limit or plot point hasbeen miscalculated or misplotted,

+ Te pece-to-pece variability or he spread ofthe distribution has increased 6, wors
ne, either at that one point intime or as part oa trend

+ The measurement system has changed (og. a different Inspector or gag.

© The measurement system lacks appropriate discrimination

A pont below
ar more ofthe

Lower contra ini (oe sample sizes of 7 or more i generally asien of one
lowing

(© The control mit or plot pin sin error.
‘Tye spread a the distribution hs decreased ie, become bette
‘Toe measurement system has changed Encoding editing alteration of the data)

Patterns or Trends Within he Control Lio = The presence ofunasun patterns or trend,
‘even when al anges are within the control iit, can be evidence of om contra change
Inpraces spread during the period ofthe pattern or rend This could give the fst warning
unfavorable conditions which shouldbe corrected. Converse, eran patterns or trends
sou be avorabe and shou bestulie or posible permanent improvement fe proces
‘Comparison of pateras between the ange and average carts mas pve added insight

Y E ap

PROCESS NOT IN CONTROL FOR RANGES PROCESS NOT IN CONTROL FOR RANGES
(LONG RUNS BOTH ABOVE AND BELOW (LONG RUN UP)
THE AVERAGE RANGE)

Figure 12. R Chat = Run (Range)

240

N. CONTROL CHARTS FOR VARIABLES
‘Section 1. X and Chars (Cont) - Interpret for Control

D

uns (See Figure 12) — Each of the folowing are signs at a proces shit or trend as he-
Les
© points in a row on one side o the average.

(© points ina row that ae consistent ineeasing (equal to o greater than the precoding
points) or content decreasing

‘Mark the point hat prompts the decision; it may be helpful to extend reference line back to
‘he begining ofthe run Analysis should consider the approximate time at which appears
that the trend or shit fist Depa.

‘Arun above the average range, ra run up signifies one or both ofthe folowing:

+ Groaterspreudin be output values, which could be from aa regular ease sua equipe
‘ment malfunetion or lose faturing) or from shift in one ofthe process element ef.
‘ew es uniform raw material 10; hese ae urall troubles that need corretin.

À change inthe measurement system (eg, new inspector or ago.

A run blow the average range, or a rundown signifie one or both of the following

(© Smaller spread in output values, which is usualy a good condition that should be studied
for vider aplication and proces improvement

+ Achange inthe measurement system, which could mask real performance changes.

NOTE: As the subgroup siz (a) becomes smaller (or leo), ho ikelihood of rans

below R increases, so run length of or more could be necessary to signal a
decrease in process variably,

-a-

€ EN «ep

PROCESS NOT IN CONTROL FOR RANGES PROCESS NOT IN CONTROL FOR RANGES
{POINTS TOO CLOSE To THE AVERAGE (POINTS TOO CLOSE TO THE CONTROL
RANGE) twits)

ll

ee en
ee ee ESS
aaa

Figure 13. R Chart - Nonrandom Patterns

a

Bw

1. CONTROL CHARTS FOR VARIABLES
Section 1. X and A Charts (Cont) - interpret tor Control

Obious Nonrandom Patterns (See Figure 13) — In ation to the presence of points be:
‘yond controllinsts or long uns, other distinct patterns may appear in he data that give es
Lo special causes. Careshould be taken nat to over interpret the ata, snes even random
common cause) data can sometimes give the illusion of nonranderness (Le, special eases
present) Examples ofnonrandom patterns could be bvious trend (even hough they di ot
Satisfy the run ests, cycles, the overall spread af datapoints within the control iis, or
‘ren relationships among values within subgroups (eg, theft reading might away o hr
ges. One ts forthe overall spre of subgroup datapoints is described below:

Distance of pins from FE: Generally, about 2/8 ofthe plate pots should ie within the
middle third of tho region between the contro limits; about LA ofthe pots shoud bon the
Outer two thirds ofthe region,

‘substantially morethan2/Sfthe plotted pint lie close to R (or 25 subgroupsifover 90%
are in he middle third ofthe control limit eon, investigate one or more of the Following.

‘The contol limits or plot points have been miscalculated or misplotted.

‚The procesor the sampling method are stratified each subgroup systematically contains

méssurement fom two or more process seams that have very dierent proces aver.

tages (eg, one pace fom each of several spindles)"

+ The data have been edited (subgroups via anges that deviated much from the average
Dave Boa altered or removed).

‘substantial over than 2/9 ofthe plotted point le clase to (for 25 suberoupsi 40% or
Teer ate in Ue middle rd, vestigate one or both ofthe flowing:

(© The control limits or plot points have been micalalted or mispltted.

©. The process orıhe samplng method cause successive subgroup to contain measurements
from two or more proces reams hat have drama dierent variability eg. mier
Tots of input material)"

several proces streams are present, they should be identified and tracked separate

See Appendix A

XANO A CONTROL CHART

| INT
n

i H laja] E

o H hehe
Mts i oo al ¿
Ki o ¿
il Fe iia RE BEBE BE i
ME A SUNT ce Él i
ns + ae i
ale | Re i
an i sleleleilelSte[al e 3
es: SE EH $

Él ue dba | e

WI cel i
: OBERE BEN i
EN SOU 5H =

. aan
de sal! i
AL ad: =
Il caia] Pi
KA | nel i
E Saler À E

pedi PEDAL

ve

O E

|. CONTROL CHARTS FOR VARIABLES
Section 1. X and Chants (Cont) - Interpret for Control

ca

cs.

Find and Address Special Causes (Range Chart) (See Figure 14)

Foreach nication of special euse in the range dat, conduct analysis ofthe operation ofthe
process to determine he use and improve proces understanding; corre! that condition, and
prevent fem recurring: The control chart tel should e a useful guide in problem ana,
Suggesting when the condition began and how long t continued. However, recagniz a no ll
spécial eases are negative that some april causes ca result in postive process improvements
{terms of decreaced variation in th range — thse special casts should be anne or possible
nsitutionlizaton within (he proces, where appropriate

‘Timelines is important in problem analysis, both in terms of minimizing the production of non
conforming output, and in terms of having fresh evidence for agnosis. For instance, the appear
inc of singe point beyond the contrel limit is rason to begin an immediate analysis of the
process. proces log may also bea helpful source of information interns of wentiying special
tures of variation,

should beemphaszed that problem solving isofen the most dictan time-consuming step.
Statistica input from the control chart can Do an appropriate starting point, ut other els
Such as Pareto chart, cause and effect diagrams, or other graphic analysis can be help (ee
‘AppendicH, Reference 12, Utimately however, the explanations or behavior lie within the proc
ds andthe people who are involved with i. Thoroughness,paence, insight and understanding
‘il be required t develop actions that all measurably improve performance,

Recalculate Control Limits (Range Chart) (See Figure 14.)

en condoctngan inital process study ora reassessment of process capability, the control it:
its shouldbe rcalalated to cache the effect of out-of-control prods fr which proces cases
ave been clearly idented und removed or insittionaize. Exclude all subgroups affected by
he special causes that have en identified and removed or institutionalize, then recalculate and
‘he pot the new average rang (R) and control mit. Confirm tha al range pints show contr!
when compared tothe new iit, repeating the identifeation/corrrtion reealelation sequence
necessary.

Ifany subgroups were dropped from the R chart because o idet special causes, they sho
also be excluded from the X char. The revised K end X should be wed to veclcuat the trial
control lit for averages, KA

NOTE: The exclusion of subgroups representing unstable conditions snot just throwing
“vay Dad data” Rather, by excluding the points allected by known special cases, we
have a better estimate of the background level of variation du to common eases
‘This, in turn, goes the mot appropriate bass forthe coatol limits use to detect
future occurrences of special causes of variation, Be reminded, however tthe
process must be changed othe special cause will ot recur GF undesirible) as par
ofthe process,

Y E <p

PROCESS IN CONTROL FOR AVERAGES PROCESS NOT IN CONTROL FOR AVERAGES
(A POINT BEYONO THE CONTROL LIMITS)

Ez ASE)
Moca ETE
ME = A == =

Figure 15. X Chart - Points Beyond Control Lit

-46-

DJ

ll. CONTROL CHARTS FOR VARIABLES
Section 1. X ans R Chars (Cont) - Interpret for Control

ca.

‘Analyze the Data Plots on the Averages Chart

"When the ranges aren statistical control, th proces spread — the ithi-subgroup variation —
isconsideredtobestable The averages ean then be analyz to se Ft process location chang.
ing overtime, Since control limits or X-bar are based upon he amount of variation in the ranges,
then ifthe averages are in statstial contre), air variation i related tothe amount variation
seen inthe ranges — thecommon-caus aration of thesystem IF teaverages ar ot in control,
Some special eases of variation are making the proces location unstable

a. Points Beyond the Control Limits (Soo Pure 15) — The presence of ne or more pats be
‘yond ether control mt is primary evidene ofthe presen of pec causes a that pola. It
'Sthesignel or immediate nabs af the operation, Mar such data points on he char (ee
page 39)

A point beyond ether control iit is generally sign of one or more of the following:

+ The contol init or plot point are i error.

© The process has shifted, ether at that one point in tie (possibly an isolate inchen or
as pare of tend

+ Tie measurement system has changed (og, diferent gage or inspect)

a

€ EN ap

PROGESS NOTIN CONTROL FOR AVERAGES PROCESS NOT IN CONTROL FOR AVERAGES
LONG RUNS BOTH ABOVE AND BELOW THE (LONG RUN UP)
AVERAGE

ce a
[ox 6810616) FE
ee has a cu
* Ss
~ = =
= = ==> == |

Figure 16. X Chan - Runs

-48-

ee

1 CONTROL CHARTS FOR VARIABLES
Section 1. X and A Charts (Cont) = Interpret for Control

Patterns o Trends Within the Control Limits — The presence of unusual patterns o trends can
evidence of non-contra during the period ofthe pater or rend. Comparison of patterns be
‘een the range and average charts may be helpful

Rune (See Figure 16) — Bach ofthe following are signs that a process shit or trend has be

sun

2 points in a row on ono side ofthe average.
© points in a row hat are consistently increasing or decreasing.

Mark the point hat prompt the decision; it may help o extend a reference line o the point

at which the run began Apalyss shoud consider the time a which ie appears thatthe rend
for sift fat began,

‘Arun relativo tothe proces average is generally a sgn of one or both ofthe following:

(© The proses average has changed ~ and may stil be changing.
© Te measurement system has changed (ri, it, semi, st).

-#-

PROCESS NOTIN CONTROL FOR AVERAGES PROCESS NOT IN CONTROL FOR AVERAGES
(POINTS TOO CLOSE TO THe PROCESS (POINTS TOO CLOSE TO THE CONTROL

AVERAGE)

Luro]

Kanon, CHART

en =

(Een ae arme) |
+:

LTR)

Figur 17. X Chart = Nonrandom Patterns

Ev

1. CONTROL CHARTS FOR VARIABLES
‘Section 1. and A Chars (Cont) = Interpret for Control

Oboious Nonrandom Pater (See Figure 17) — Other distint patterns may aso indicate
the presence of special use of variation although care mus be akon nat to ovr-interpre
{De data Amongthese patterns are trends cycles unusual pred of pants within the control
Tits and relations ip song luce within subgroupe. One tet or unusual spread ls given
below

Distance of points from the process average: General, abou 2/3 ofthe potted point should
liewithin the mile id ofthe region between the conto! iit about 19 ofthe point wi
beintheouter two-thirds ofthe region: about 1/20 willie relatively cose oho control its
in heouterthirdoftheregion) Also, he probability exists at about 1150 coude outside
contol limits bat still be legitimately par of a stable sytem in controlo, only about
99.78% ofthe points wil be within he contro! mit,

IE ubstantaly more than 2 fe points else tothe process average for 25 suberoupsit
‘ver 90% are inthe mid third ofthe control limit region) investigate ae or mare of the
following

+ Thecontrllimitsorplat points have ben misraleulated, misploted, or incorrectly eal

‘© Theproces or the sampling method are stratified each subgroup contains measurements
{rom two or more process streams that have dierent averages
+ Tho data have been elite

substantially fever than 29 ofthe data points le eos o the process average or 25 sub
groups iF 40% or fewer ar ia the mide thie), investigate one or both ofthe fallow:

‘The control limits or plt points have been micalculted or misplotted.
‘Theprocessor the sampling method cause successive subgroups to contain measurements
rom two or mare very diferent proces steams" (hs an bathe result of overcontro of
an adjustable process, where proces changes are made in response to random aca
‘ons in the process data"),

several process streams are present, they should be identified and tracked separately.”

es example in Appendix A
ee example in Appendix .

a

XANO R CONTROL CHART

EINES

À

Pt dido!

Figure 18. X and R Char - Control Limits Recalcutatión

1. CONTROL CHARTS FOR VARIABLES
Section 1. Zand Char (Cont) - Interpret for Control

2. Find and Address Special Causes (Averages Chart) (See Figure 18)

For each indication ofan out-of-control condition in the average data, conduct an analysis ofthe
‘operation ofthe process to determine the reason forthe specal case; correct that condition, and
prevent it from recurring. Use the cart data as a guide to when such conditions began and how
long they continued. Timeliness in analysis is important, bth for diagnos ando minimine non.
conforming output. Again, be aware that nat al special eases ned bo undesirable (se Page 45,
Section C2

Problem solving techniques such as Pareto analysis and eause-and-eet analysis can hel. (Soe
Appendix H, Reference 11)

6. Recalculate Control Limit

Averages Chart) (See Figure 18)

When conducting am nti proces study or esssossmentofprocss capability, exclude any out-
“control points for which social eases have been found and removed; recalculate and plot the
proces average and control limit. Conf that al datapoints show control when compare to
{hs new lis, repeating the Wentcatin/correcion/recalculstion sequence IF mece,

"The preceding discussion were intended to give a functional introduction to control chart analysis. There
are, however other consderaions that can be vel tothe analyst. One of the most important the
‘minder that, even with processes hat are in statistical contre, as mare data are reviewed, the constant
‘chances of giing a false signal fa special cause on any individual sbproup eranlae to iereasing ike
hood of finding falo signal somewhere on the char).

While is wise to investigate al signaled events as posible evidence of special causes, it should be recog
ized that they may have bean caused by the system and tha here may be no undeeying cal process prob.
em. no clar evidence of proces special causes found, any “corrective” ation vl probably servo to
‘creas, rather than decreas, the total variably inte process output

For further discusion of interpretation, ets for randomnes in data, and problem-solving, es Appendix
Ho References 1-39,

Figure 19. X and R Chart - Extended Lins

1. CONTROL CHARTS FOR VARIABLES.

Section 1. X and A Chats (Cont)

©

cs.

Interpret or Control
[Extend Control Limi

for Ongoing Control (Bee Figure 19)

When the itil Cor historia data are consistently contained within the til contra limits, x
tend the its to over future periods. Te might be desirable hereto also adjust the process tothe
‘ane he process center sof target See page 22). These limits would be und for ongoing moni.
toring ofthe process, with te opertorand al supervision responding to sis of out-of-core
conditions on ether the X or R chat th prompt action.

A change inthe subgroup sample size would alt the expected average range and the control
limits for Both ranges and averages. This situation could ocur, fo npanor, as decido
tale smaller samples more frequently, 5 as detect arg process sis more quickly without
increasingthetota number o peces sampled per day. To adjst central lines and control mits for
ew saberoup sample sie, he following step should be taken:

a. Bstimate the process standard deviation (o estima is shown asd — “sigma ha), Using
‘he existing subgroup size calcula:
C7

‘where F istheaverage ofthe subgroup anges fr periods with the range in contre and dis
“constan vaine sample iz, ax shown In the partial tao below taken rum Appendix:

at2[s]4]s|e6]7]e] es]
a | ía | res | 206 | 235 | 265 | 270 | 285 | 297 | 908

b. Using the abled factors ford, Ds, Da, and Az based on the nes subgroup size, calculate the
en range and control its

LCL = Dahn

UCLA + Ake

Lege = AR

Plot these new contol limits on the chart ns the basis for ongoing proces control,

[As lomas the proces remains in contol for bath averages and ranges, th ongoing limits can be
extended fr ational periods however, there is evidence thatthe process average or range
has changed in either direction), the cause shoul be determined and, ifthe change usb,
‘contol mis shouldbe recalelated based on current performance.

Final Concepts on “Control” - For Further Consideration

A perfect stat of controls never attainable ina production pocos. The goal ofthe process con
ol charts isnot perfection, but a resonable and economical state of contra, For practic pr
posts, therefore controlled process isnot one where the chart neve: goesoutof contra Ifa chant
Hever went out of control we would seriously question whether tht operation should e carted.
Forshop purposes controled process isconsferedtobeone where ony mal percentage ofthe
points go out of control and where ot-of-contro points are followed by proper ation = From
‘Appendix He Reference 7, page 220-221)

Y E E>

ee oo ee sa
E = i i

H ! i i

i | i i i

i i i i

Figure 20. Process Variation Relave To Specification Limits

-8-

la CONTROL CHARTS FOR VARIABLES
‘Section 1. and A Chars (Cont)

Obviously, there aredteret levels o degree of statistical contro The definition of eontrol used
an range ram mere utliers(eyond Use control mit), through runs, trends and train,
oil zone analysis As the definition ofcontrol wed advances tofu zone analysis the ik
offinding lack af onto! increases Tr example, a process with no alles may demonstrate Jak
‘teontro through an obvios un stil within the contra limits), For his reason, the definition of
‘control usd should be consistent with our bility to detet this atthe point of contra and should
‘emai the same within ne time period, within one process. Some suppliers may not be able to
apply the fuller definition of control oa the Mor on a real-time basis ue to immatur stages of
Operator training or lack of sophistication inthe operators ability. The ability to detect ack of
(ontrolat the point ofcontrolena real-time basis an advantage othe contol chart Over-inter-
pretation ofthe data can bee danper in muintaninga true state of economical contra,

D. INTERPRET FOR PROCESS CAPABILITY

‘To continue the example from Figure 18 an interpretation for process epabit willbe discussed, under the
folowing assumptions:

+ The process is statistically stable
+ The individual measurements from the process conform tothe normal distribution
+ Me engineering and other specifications accurataly represent customer needs
The design target iin the center of the specification width

(© Measurement variation i relatively small

Having determined that a proces iin statistical contro, the question stil remains whether the process
capable of meeting customer neds. To understand and improve the capability oa proces, an Important
Shin thinking mt occur cpabity reflect variation from common causes, and management action on.
‘the system is almost always required fr capability improvement See Figure 20)

Assessment af proces capability begin after control sues in both the X and R chart have been sole
(special causes dente, analyzed, corected and prevented from rcurrng),and the ongoing control chats
reflet a process that in statistical control, preferably fr 26 or more subgraups Ta general, the istribur
tion ofthe process output is compared wich the engineering specifications, to see whether these specific.
tions can consistently de set,

‘There aro many techniques or asessing the capability of process that i in statistical control, Some a
sume thatthe prose tpt fall th alchnped normal iron Wit nat ka whether the
‘istributonis normal atest fr normality should be made suchas reviewing ahistograr, plating on normal
probability paper or using more presse methods (ae Appendix H, Reference 9, Chapter 27) 1 nomnor:
{nal is suspected or confiemed, more fleble techniques should be used, such a data transformation 10
“normalize” the distribution (ee Appendix H, Reference 18, Part 2, computerized curve-ting or raph
‘al analysis, When the distribution shapes normal the technique described below cn be used. e involves
‘only simple alulcions based on data from the contol chart. The proces average, X, is sel asthe lace
tion ofthe distribution. Asa measure of spread, the standard deviation i wed estat from a simple
formula involving the average range, R

-51-

tg

Figure 21. Calculaing the Process Capabiny

-88-

O En LT

I. CONTROL CHARTS FOR VARIABLES

Section 1. and Chart (Cont) - Interpret for Process C
NOTE:

. Caleulate the Process Ca

y

Any capability analysis technique, no matter how precise it appears, can give only
‘approximate result. This happens because (1) there i always some sampling variation,
(Do proces e ever Taly” Im statistical control and (9) no actual output “exactly
follows the normal distribution (or any other simple distribution) Final results should
a be und with ution and interpreted conservatively

. Caleulate the Process Standard Deviation

‘Since the within-subgroup process variability is reflected in the subgroup ranges, the estimate of
‘theprocess standard devitiond sigma hat” canbe based onthe average range (Callate:

Ré, = Or,

‘where Kis the average of the subgroup ranges (or periods with the rangs in conteo) and d isa
‘Constant varying by Sample size, as shown i the partial table below, taken from Appendix E

nielsleals]esl | s] +7] 7%
a [ais tes | 208 | 293 | 285 | 270 | 285 | 267 | 308

‘This estimate ofthe process standard deviation ($) can be usd in evaluatingthe process cpu
‘lity, a Tong az both the ranges and average rein statistical control

bility (See Figure 21)

CCapabiliy can be describa in terms ofthe distance ofthe process average from the speciation
[mits in standard deviation wits, 2. Drawing a diagram that shows the distribution eure, X,

ut, the specication limits and the values wil e help
USER | Rots

on Er

® Forauniatealtoerane,caculite:Z swhicheverisapproprate

‘where SL = speciation limit, X = measured proces average and = estimated proc
‘es standard deviation,

© For bilateral tolerances, eaeulate:
WER „Rust
C7 C7

Lon

Zan = Minimum of Zo or Zen.

where USL, LSL = upper and lower specication limit; a negative value of Z indkates the
process averages outa specication

‘values can be used with tale ofthe standard normal distribution (Appendix Ft estimate the
proportion of output that wil be beyond any specification (an approximate vale, assuming that
‘he proces isin satistica control and is normally ditribated.

‘© Foraupilateral tolerance, locate the value of along the edges ofthe table in Appendix. The
‘unite and tenths digits are along the Jo ed nd tho hundredths ii along the top The
number found wher his row and colma terse is pr, Ue proportion outa peiicton
Forinstance for = 1.56 the intersection ofthe 1.5 ow and>ex column ies pz = 0594, oF
about 6%

-9-

vu

From the example

eho spa requirement, expressdiaterms of Zu vas Zu 2 4 henthocurrent process capably,
ems of Zu, woul be unaceplabl since Zu = 228 and about 1 3% a output ie beyond pecan:
| even fie procs could be center, Zu, = 276 Action must be ta.

+ Toimprove actual proces capability (Ue lng-term goal, the variation from common causes must be
duced this would be measund a smaller

‘The present proces average X is usd to ala the spread necessary for Zu = 4 elatve tothe
‘eating porfas

can
E

which speciation it iscloter othe process
‘sverige Sine ere the USL ste cases mie

EA

This means that actions must b taken to reduce bo process
standard deviation rom 0725 0.0405, Ah 4% Improv

confirmed by control chars that the process has ben center, and Fa = 700, the process pre
ocean für Zu » 4 (X & do) based on the exiting spcifatons vou be
300-700 . 200 4

EE

With pros adjustment tothe center o the specifications,
actions would be ende toreducs the proces standard dvi:
(ion from 0725 10500, about 81%. 4

+ Watlouput eo be sorted, aout 13% (aboot. centered) must be srappa or reworkc iis
expensive snd ure

some cases, a short-term alternative coud bet nerus the specification toleran.

Ifthe pocas not tobe changed, new 4 do specfestions
sro be

Radon ma 4x 072 = 738 4 290
= 44610 1.025 Rounded: 45 to 1.09)

the process hs ben adjusted and has been cone by
contd harta that Rie =-700, (centered), new Ke 49
Spetcatns wold be
Fono 2402.70 à 4x 0725 = 700 4 290
= 1010.90 (und 4010 1.00

Figure 22. Evaluating the Process Capabiity

-00-

O ES í

1. CONTROL CHARTS FOR VARIABLES
‘Section 1. X and R Chars (Cont) - interpret for Process Capabiaty

Da.

+ Poratilteraloleranc,clclae the proportion beyond upper and lower specication im.
its separatly For example, if Zu 2,21 and Za = -2.85, the total beyond specifen-

on is Peon. * Pras. = 0158 + 0022 = 0158, or about 1

‘The value Z,can alo be converted toa Capability Index, Ca, defined as:

Minimum of cPU (ie. USE =) or cov (i.e. ELSE
ne en ER) wen (1

‘where USLand LSL ar theupperand lower engineering speciation, isthe process verga,

Cae

iit oneal oat ae a

A process with Zu» Swould havea Capabiity Index Ca = 1.00.1 Zu = 4 the process would
have Cp = 138,

Evaluate the Process Capability (See Figure 22)

Abi point, the process has ben brought int statistical contra andits expat index has been
described in terms of Za Coa The nest step ft evaluate the proces capability in terms of
meeting customer requirement,

‘The fundamental gal is never-ending improvement in process performance. In the near-tr,
however, priorities must be set as to which processes shoud receive attention ft. Tiss essen:
tally an ronomiedeiion. The eireamstances vary from ase o cae, depending on the nature of
‘tho particle process in question and the performance of other processes which might alo bo
‘andidates for immediate improvement action,

‘While each decision could be resolved individual, i often helpful to use broder guidelines to
‘ot prioriis and promote consistency of improvement effort. For instane, ertan procedures
refer to across-the-board capability index requirements of Za 2 3. 01 Cp 2 1.00, and fre
ther specify capability index requirements of Zu, 2 4, oF Cp 2 1.33, forme procensesaifet-
ingsleced significant product characteristics These requirements areintended to assure mini
‘mam performance level that i consisten among characteristics, products, and manufacturing
Sources However, please refer ta Section of thisehaptr for more understanding the interpre
tation of the Ca and other process measures relative o establishing measure retirements

‘Whether in response toa capability index criterion that bas not been met, r to the continuing

noe fr improvement feat and quality performance beyond minimum capability index require.

‘ments, the action required the same

© Improve the proces performance by reusing the variation that comes from common causes,
‘or shift he process average closer tothe target. This generally means taking management
conto improve the system

Inthosecases where moreimmediateaction sneceasary to meat short-term needs, S40 Stop aps
may be available

+ Sort output and sap or rework as necessary (hus adding cost and tleraing waste)

+ Alter the specications for consistency with the proces performance (his improves neither
‘the proces or customer satiation)

‘These ae both clearly inferior t process improvement.

sae

IMPROVE THE PROCESS CAPABILITY

‘To improve the capabiity (and thus, the performance) of the
process, concentrate on reducing the common causes.
‘These will usually require management action on the system.
to correct.

CHART AND ANALYZE THE REVISED PROCESS

Confirm the effectiveness of system changes by continued
monitoring of the control chart.

M. CONTROL CHARTS FOR VARIABLES.
Section 1. X and Charts (Cont) - interpret for Process Capabitty

Da.

Ds.

esprove the Process Capa

y

"improve process capably, there must be increased attention on reducing common causes. Ac:
Lions must e directed toward the system, namely, underlying process factors which acount
forthe process variability suchas machine performance, conssteny of input materials, the asie
‘methods hy which the proces operates traning methods, or he working environment. Asa ge
al ral, these system related causes or unacceptable proces capability may be beyond thea:
tis of operators or their local supervision to correct. Taste, they may require management in
tervention to make asie change allocate resources, and provide the coordination nrded to im.
prove the overall proces performance, Attempts to correct the system with short-rangelocalac-
ons wil be unsuccessful

Discussions of techniques for analysis of system variability are included in sevra of the refer=
‘ences std in Append H.Hase problem-solving techniques suc s Pareto analyse and causo
and analysis can be helpful ee Appendix H, Reference 1) However, seo! more advanced
methods of proces analysis including statistical techniques such as designed experiments may be
necessary to achieve significant reductions, See Appendix References 7-18 fr introductions to
Some of these more advanced methods

Chart and Analyze the Revised Process.

‘When systematic proces actions have ben taken, her elects should be apparent inthe control
chars, The chart become a wuy of verlying the elfectiveness ofthe action

As the process change is implemented, the control chart should be monitored caeflly. This
‘ange period canbe disruptive operations, potential causing new control problems that could
baci the effet ofthe system change

“Alter any instabilities ofthe change period have been resolved he new proces capabliy should
e ssesed and used as the bass of new contol limits for future operations. Frequently. 25 sub-
groups of data ler the change ae sufheent to sta the new contol limit.

va

DR Cou PER OE Om)
SMLE-BRE 10 CONSECUVE PR GES THE PER ON"
+ [1301101] 422 108120] 1.25| 1:20] 1.13] 108
2 riof of vos iso| 134] 62[ 30) 001030 26] sn
ER LESERN 113] +19] 1050000) [aol 132| 132
[loros 103] 113] 120] 1.0) 100128) 122| 130
5 ros[12s 0.0] oaf von] 9a] 118] 142|138
= [ss] aa 17 | use| 04.25.09] 1.5] of sar
[role 24] 195] 541.20] +29] 108[108[ =
Te 1.46] 90 1.08| 1.24 | 1.42 1.02| 1.28] 1.05
ofr oe 34]. 132[ 130 430|108[122[ 100
CRE 112] 505[100[ 109] 100/1:0[130|120
3 Tune 19] 15] 06] of vof sae] is
5 08] 0620241] ef on ora] 70] sas] ore nur
Jonas sal or) vaa]
2 [28] aa] nos] m
> rs] ae] sae] sfr
A ‘aa
> [im 10] 140
Tes waa
7 1.07 1.02| 1.15] E
of uaa 09] on
PC COTE
10 | #18] +36] +00] 136| 100 1.14] =
11a] 1.12] 1.08] 1.18] 1.06 | 1.13 i.
[001 saone rer] -

Figure 23. Dala Cotection

-

O E Y

Section 2
AVERAGE AND STANDARD DEVIATION CHARTS (X AND s)

X ands chat ike X and charts ar developed from measured process output daa, andre lys sed
“asa pair. Range chars were developed as measures of process variation because he range is easy to calculate
tnd is relatively efficent for small subgroup sample sizes (especially below 9). The sample standard evi:
tion sis amore efficent indicator of proces variability, especially with larger sample sizes. However, its
‘more complex to calculate, ad its es sensitive in detecting special causes o vation that cause only a
Single value ina subgroup to beunusual Typically s charts are used instead of charts when oneor more
‘the folowing et

+ Thedataare recorded andor charted by computer on a real-time basis, soa calaltion routine for i
easly integrated

+ Ready svalbity of pocket calculator makes computation o simple on a routine basis
‘Large subgroup sample sizes are used, and the mare efficient measure of variation is appropriate.

‘The details of instructions for X and s charts are very similar to those for X and charts; exception are
noted below,

A. GATHER DATA
(Gee Section 1, Part A of this chapter, exceptions are noted below)

(© Lrv data re voluminous, they are often recorded ona separate data sect (ee Figure 20), with
on each subgroup's X ands appearing om the char sel

‘+ Calculte each subgroup's sample standard deviation using one of the following equivalent

where X „X, and represent the subgroup’

vidual values, average, and sample size
NOTE: Do not round of values if omputing lnghand

© The sale spacing for thes char shouldbe the same as for its corresponding X char.

-05-

RAND e CONTROL CHART

===|
= =
= =]
E >
)
/
SESE

Figure 24. X ande Chan

-66-

> En Y

11. CONTROL CHARTS FOR VARIABLES

Section 2. X ands Charts (Cont)

B. CALCULATE CONTROL LIMITS (See Figure 24.)
(Sei Section 1, Part B o is chapter, exceptions are noted below)

“+ Calculto th upper and lower control Limits for standard deviations and averages (UCL, LCs,
UCLR, LEI

Ucty= Bs
pS

Las

Leis RAF
where ¢ isthe average of the individual ubgroup sample standard deviations, and By Band Asare

“Constants varying by sample size, with vals for sample sigs 210 10 shawn In the lovin portal
Fable taken from Appendix E

n 2 I 3 4 5 6 7 a 9 |
Ba | 327 | 287 | 227 | 209 | 197 | 188 | 182 | 170 | 172
A A O + | ol ES
As | 266 | 195 | 160 | 100 | 120 | 118 | 1:10 | 103 | 08

+ Therein lower contro limit fr standard deviations fr sample sizes below 6.

©. INTERPRET FOR PROCESS CONTROL

(See Section 1, Part C of this chapter)

D. INTERPRET FOR PROCESS CAPABILITY
(See Section, Part D ofthis chapter, exceptions are noted below)
1 Estimate the process standard deviation:
B= She à Sing
where & is the average ofthe sample standard deviations fr periods withthe standard deviation

Under control and isa constant varying by sample sine with values for sample ins rom 28019
‘shown in the fllowig pata tale, taken from Appendix E

[ESO IE O O A EC E
>|] 00] 25] 20] 35] 25] es [aes [ara

lethe process as a normal distribution this estimate of can be used directly in assessing process
‘capably, as ong as oth averages and standard deviations are i statistical contol

as

oS E>

Figure 25. Mecian Control Chart

08.

> EN ET

ll. CONTROL CHARTS FOR VARIABLES.

Section 3
MEDIAN CHARTS (X AND R)

Median charts(sce Figure 2) are alternatives to X and R chart for contol af processes with measured
data; despite the fact that medians may not be as statistical desirable ns average, median chars yield
Similar conclusions and have same advantages

‘Median chart are easy to use, and donot require many calculations This can increase shop-loor
acceptance o the control char approach.

‘©Since individual values a weil a medians) are potted the median chat shows the spread of prue»
es output and gives an ongoing picture ofthe process variation

(© Sincea single chart shows both the median and spread, ican be usd to compare the output of ve
‘er processes, o ofthe same process at successive stages

Instructions fr median charts are similar to X and R charts; exceptions ao noted

A. GATHER DATA
(See Section 1, Par A ofthis chapter exceptions are noted below)

+ Typicaly, median charts ae used with subgroup sample sizes of 10 lose dd sample sizes are
most convenient, sing even size subgroups, the median i the average ofthe middle two units

+ Onlya single graph maybe plotted se th cal include he larger of the product specification
tolerance plus an allowance for out-of-specicatin readings, o D) 1-1/2 a mes the direc
Between the highest and lowest individual measurement. The raph sales should agree withthe
mes

© Plot tho individual measurements fr each subgroup in a vertical line. Circle the median ofeach
Subgroup he middle value: if sample size sam even number, he median vil be may between
‘the inne points). To al in interpreting trend, connect the subproup medians by ane,

© Enter each subgroop’s median (X) and range () in the data table. Tis recommended to also plot
‘the range chart to observe trends or runs ln the range,
B. CALCULATE CONTROL LIMITS
(See Section 1, Part B ofthis ehaper exceptions are noted below
Find the average ofthe subgroup medians and draw this a the central lin on the char; record this
ask
© Find the average ofthe ranges record this as R.

+ Cateulatetheupperand lower controllimitsforranges and modians (UCL, LCL, UCIZ, LCL)
Cty = DAE

LC = DR
vet KX
1er

oR

Figure 26. Median Control Char - interpretation

-10-

> =
1. SONTROL CHARIS FoR VARADIES

‘Section 2. Median Chart (Cont)

where Du, Da. and Xz are constants varying by sample site, with values forsale sizes 2 t 10
Shown inthe following table, taken from Appendix E.

E O AO O CI A ICI CO
De] sar | ear] Beef att | 200] Tee | 188 | 182 | 178
olen toe fo [oe |e | "oe | se | te | ze
else | sie | sol solos] i) ao | os

"There is no lower control limit for ranges for sample sizes below 7

+ Plot the contol limits for medians on the chart.

(©. INTERPRET FOR PROCESS CONTROL

(See Section 1, Part C ofthis chapter exceptions are nated below

© Compare the UCL and LCL with each calculated range Alternatively, mark the edge ofan index
‘ard with the points corresponding tothe contr limits for ranges, and comparo these marks with
the distance between the highest and lowest vale in each subgroup, Diva narrow vertical boto
enclose any subgroup with excessive range

‘Mark any subgroup median that is beyond the median conrolimis, and note the spread endian
‘within the control mis (23 of points within middle third o mis) orth existence of patterns or
{rend Gee Figure 26,

‘© Take appropriate process action for special uses acting the ranges or medias.

D. INTERPRET FOR PROCESS CAPABILITY
‘See Section 1, Part D ofthis chapter; exceptions are noted below)
(© Bstimate the proces standard deviation:
> RU
here Kis the average of the sample ranges (or periods with the range under control) and isa

Constan varying by sample ie, sith values for sample ies frm 2 o 10 shown i the following
Fable taken from Appendix E

el[2[s]«]s]|e6]7] se] +]
de | 113 | res | 206 | 235 | 255 | 270 | 205 | 297 | 908

+ tebe proces asa normal distribution, bis estimate af an be used directly in assessin process
‘capably, a long as tn medias and ranges are in statistical contra

one

vu

1. CONTROL CHARTS FOR VARIABLES.
Section. Median Charts (Cont)

E. ALTERNATE APPROACH TO MEDIAN CHART

For ongoing process control where contro limits ao based on prior dato the charting process can be
implied as flows

‘© A single chart is used, with sales stat the same increments asthe gage being used (at east 20
increments between product specifications), and withthe central in ad contra imi for medians
already entered

‘+ Acard possibly plastic is provided, marked with the control mit for ranges. Tis assumes the
‘special eases affecting the ranges generate Ow of control points and nt trends,

{© The operator marks the chart wth each individual reading bt the meré values donot need to
be recorded

[© For each subgroup, the operator compares th range card to the subgrouy's highest and lowest
marks; any subgroup having range beyond the its onthe cad is enclosed in a arrow vertical
box.

+ Theoperatorcountstothe median ofeach subgroup andcirlesit any median beyond either control
limit fe marked

‘= For ranges or medians beyond contro! its, the operator takes appropriate ation o adjust or
‘correct the process, orto notify supervisory or support people

-n-

9 MOVING RANGER CONTROL CHAR "nm STUDY

pence te nor cna

us

Figur 27. Individual and Moving Range Chart

Ae

1. CONTROL CHARTS FOR VARIABLES
Section 4
CHARTS FOR INDIVIDUALS AND MOVING RANGE (X-MR)

In some cases, ti necessary for proces control tobe based on individual readings, rather han subgroups.

Insuch cases, the within subgroup variation effectively zero, This would play cur hen themenaure
ments ar expensive ea destructive tet, or when the oulput a any pnt in time is relalvely homoge
nous eg, the pH ofa chemical auton). these caves, contra charts for individuals un be constructed as
described below, Four cautions should be note, however,

+ Charts for individuals are notas sensitive in detecting proces changes as X and R chart.

+ Caromustbetaken n interpretation of chars for individuals ithe process distribution not ymmete
ai

Chart for individuals do not slate te pics-to-plece repeatability ofthe process, In many appli

‘ions, therefore may be beter tn use a conventional X and chart with small subgroup sample sizes
(210) even tis requires à longer period betwen subgroups

‘+ Since thereisonly oneindividua item per subgroup, values of X und can have substantial vibility
(even if the proces is stable) until the number of Subgroups is 100 or more.

‘The details of instructions fo charts for individuals are somewhat similar to those for X and R charts ex
espions are noted below:

A. GATHER DATA (See Figure 27.)
(See Section 1, Par A ofthis chapter exceptions ae nated below)
Individual rendings (0 are recorded from le to right on the data chart

+ Calclat the moving ange (MR) between individuals I generally best to record the difference
‘between each successive pair o readings (eg. difference between the rt nd second reading, the
second and third te) Thee willbe oe less such moving range han here are individual readings
(@5 readings give 24 moving ranges) Ia rare case, the moving rang can be based ona larger moving
group eg, thres or fours), or ona fixed subgroup (al the readings taken on single shi)
Note that eventhough the measurements are sampled individual, ts the number 0 readings
Graupedt form the moving rang eg, 2, or 4) which determines the nomial samplesizen Ths
‘st be considered when consulting factor tables,

2 Sec scales forthe char far individuals 0 equal to helanger of) the product peccation tler
‘nce plus an allowance for out-of-specifcation readings, o 1) 1-1/2t02 times the difference be
en the highest and lowest individual readings. The sal spaciog forthe chat for moving ranges
(EHD should be the same as that of the X char

B. CALCULATE CONTROL LIMITS (See Figure 28.)
(See paragraph B, Section 1 of this chapt

exceptions are noted below
+ Catelate an plot the proces average (the sum of individual readings, divided by the number of
readings; by convention, labeled: see the Glossary in Appendix ), and alle the average

range (note hat fora moving range ofsamplesizetwothereisoneless moving range valve MR
{han te number of didn reading» OÙ.

va

INDIVIDUALS AND MOVING RANGE (MR) CONTROL |

= O 1" Van |
ar A
i CIT
ns SN
PE mg
MES === Er.
¡PRESS
|» SH
+ +
n
FE t

“ost arg ns es suo prom woe bt rer crecio

Figure 28. interpretation of individuals and Moving Range Chart

-1-

O ES

4, CONTROL CHARTS FOR VARIABLES
Section 4. Individual and Moving Range (X-MA) Charts (Cont) - Caleuiate Control Lits

© Calelato the control init:
VCD
LL DE
VOL +e
LcLa= EJ
where isthe average moving range, X is te process average, and Da, Dy and Es are constants

that vary according tothe same sie, used in grouping them rampe, shown Lolo
Ing partial table, taken from Appendix E.

E OC CA A CC CA A A E
Bel Bar| ar] Bae UE IE AE IE IE
ee ed E
ta Lacs | oz | rae | ao lol sit | sae | var | à

‘Ther is no lower contol Imit for ranges for sample izes below 7.

NOTE: An alternate approach to calculating control mit when R i greater than the median
range, B as is generally the eas) sto use the median rage for 2 pisce moving
rangés and compte control limits a follows (se Appendix I, Reference 2)

Ubu =3.865 E: Lele 0
Veiga Kaas; Leia R-2.14%

©. INTERPRET FOR PROCESS CONTROL (See Figure 28.)

(See Section 1, Par C ofthis cbaptor exceptions are note below)

Review the moving range chart for points beyond the control iit as signs ofthe existence ofspe-
tial causs. Note that sucessive moving ranges ar correlated inc they have atleast one Pantin
commons because of this, care must be taken when interpreting tends, Advice From à ta
might be required for trend interpretations,

‘+ The chart for indviduts can be analyzed for points beyond the control mits, prea of points
within he control nts, abd tends or patterns, Note hee, though, that the process distribution

isnot symmetrical, theruls chow previously for X chart may give signals of special causes when

D. INTERPRET FOR PROCESS CAPABILITY (See Figure 26.)
(See Section 1, Part D ofthis chapter exceptions are noted below)
As th X and R charts, the process standard deviation can be estimated ty:
= Rd: = Oe,
‘where is the average ofthe moving ranges and dz isa constant varying bythe sample ie, used

in grouping the moving ranges as shown inthe partial tale below, takes fom Appendix E

Section 4. Individual Cha (Cont) - Iterpt for Process Capebitty

eav~2—[s[ «| s]e|[ 7] e] eo] 0
ee [us [res | 200 | 20 [ass | 270 | 205 | 207 | am

+ Irthe proces has anormal distribution, this estimate of can be sed directly in seing process
capably, a lomas Le process iia statistical control,

> a

|. CONTROL CHARTS FOR VARIABLES
Section 5

UNDERSTANDING PROCESS CAPABILITY AND PROCESS
PERFORMANCE FOR VARIABLES DATA

‘The output ofa statistical table in contro) manufacturing proces can be described y it distribution
Characteristics ofi distribution aro usado evalte the process Forinstanc,acharactorisicol frequent
interest the conte ofthe distribution. I the distribution en property located, ho manufacturing proc
es may produce parts hat are not close onough toa desired target var. In such ass, some parts may ave.
‘eout-af-specication A proces with sucha distribution may then be assess as incapable of meting be
customer need. Similar problems may occur the distribution has too much spread, regale of where
‘the distributions located. Because he characterises of the distribution are no know exact, data must
be gathered to estimate them.

‘This section adresses some o he techniques used or estimating how certain ofthe characteristics ofthe
distribution relate o specifications. The underlying pre-condition thatthe proces rom which the data
came exit statistic stability should be reemphasized here. A discussion of proces variation and the
“associated capability indice has tl va for unpredictable processes. Br aware howere, that esconable
approaches for asessing process capability have Deen develope for procesn abibiting atea special
‘huss of process variation, such as too! wea (see Appendie H, Reference 12. In adi, se generally
sue hat ee individ readings frm the sujet proceses havea distribution thats approximately
normal. Alter defining proces capabilty and related terms, this section vil deine and discs any the
‘more popular indices and rates, a allows

Indices of process variation only, relative to specifications: Cy and Py
Indices of proces variation and centring combined, relative o spaciications: CPU, CPL, Ca amd Pa
Ratios of process variation only, relative to specifications: CR and PR

NOTE: Although other indices are not discussed in this manual, Appendix D and Appendix H,
Reference 18 do provide information on one of these, Ca reatvely new index
‘which has gned some recent attention
Finally this section describes the conditions and assumption associated with these process measures
and concludes wth a suggestion sto how these measures might be apli toward enhancing proces
“understanding within the framework o continual process improvement,

"This manual fly recognizes bot the misunderstanding nd controversy which surrounds fundamental
concepts and definitions ative tothe sues of process “Contra” “Capability and Performance: 1
As appropriate to point out here that its not the purposeof this manual to ul resolve these ses, but
o expose and ions them to an extent which allows each reader the opportunity ta develop beter
understanding af them in order to provide valve and knowledge fr continua proves improvement

A. DEFINITION OF PROCESS TERMS

‘Inherent Process Variation — That portion of process variation due to common causes only. This
variation can be estimate from control chats by R/d, among athe thing (eg. 51)

‘Teal Proves Variation — This is he variation due to beth common and specie uses. This var
ation may be estate by 5, Ch sample standard deviation, using al a he individual endings ob

tained fom either detailed contol chart or» process udn, 5 2 ds here

X, san indsidual reading sho average of te individu readings and = the total mimber af
A of the individual radins.

ve

|. CONTROL CHARTS FOR VARIABLES
Section 5. Understanding Capanity (Cont) - Definiton ot Process Measures

‘Process Copablty — The o range of proces inherent variation, for tail stale proc-
ses only, where url estimated by R/d: (u)

(© Process Peformance — The 6 orange fa proces total aration where vis usually estimated by
4 the sample standard deviation (i).

DEFINITION OF PROCESS MEASURES
BAL Indices
©: Thisis the capable which is define as the tolerance width divided hy the process
capability, irecpctivo of process centering. Typically, this is expres as
USL-LSL

Ge
7 Thisis the performance index whichis defined asthe tolerance wth divided bythe proc
sas performance, imespactiv of process centering, Typcal, this is expressed as

USL-LSL should be used only to compare to or with C and Cx and to mens.
El

re and prioritize improvement over time)

‘CPU: This isthe upper capability inde andi dei as the upper trance spre divided by

‘he actual upper proces spread. Typical, his is expresadas CPU = USL.- E
i ET

(CPL: Thisistholonercapabilityindexandis deinedasthelowertlernee prend vida y the

tal lower proces spread. Typical, his expresedas CPL = K-LSL,
Save,

et ‘This the capability index which count for process centering nds defined asthe mis
mumof CPU or CPL relates the sealed sance Between the process mean and the dos.
cet spocation init a hal he taal process pret

Bos This the performance index which accounts fr proce centering and is defined asthe
‘minimum of USL-X or X-LSL (it should be used only to compare to or with Cy and

El Ed

ax and to measure and prioritize improvement ver im)

%

(OR: This is the capability ratio and is simply the reciprocal of Cy: Le, CR =

Wrst

PR: This i the performance ratio and is simply the reciprocal of Pi Le, PR =
CA
vEL- ISE

NOTE: Example calsatoos for all of these measures are shown on page 6,

-

—————__— @ Be

‘CONTROL CHARTS FOR VARIABLES
Section 6. Understanding Capanity (Cont - Defniton of Process Measures.
BS Clarification of Sample Standard Deviation - à vs.
Both s(usedin parto A and Bof this section) and (asd in X ands chart, page 65) are called

sing exactly the samoformulaforsamplestandard devaton:Le, sand y

‘ever Chen? in the formula symbolizes tw diferent types of sample sizes, a follows:

(© For. (age 79), n efes tothe total number fal of he individual values sampled forexam-
ple, he numberof hese individual values can come from the total ofthe numberof al ofthe
Sulgroup individual values from a control chart ll totaled together) or from abroad sa
bling ofan overall population,

+ Fors (page 6), seers only tothe numberof individual vales within any given subgroup =
generlly.n ia constant and equal number for each subgroup

2 estimates the standard deviation ofa total process ("population") using , while ds et
‘ates the standard deviation of given sung of fixe sz, using (ce pages 65-07)

(©. DESCRIPTION OF CONDITIONS AND ASSUMPTIONS

kis appropriate to point out that proces variation and process centering are two separate process
charactersis Each ned tobe understood separately fromthe other. However, in order tn miimize
Separate analyses ofeach, has became canvenlent to combine the two characteristics into one inde,
such as Cya or Pa These indies can be sell fo:

Measuring continual improvement using trends over time.
+ Priorticing the order in whieh processes vil e improved,

‘Thesapailtyindex(og., Cy is additional useful for determining whether or note process capable
of meeting customer requirements (he original inent ofth expabiity inde).I shoal be pointed out
that this additional use should nat be applied to performance indices see page 60 for suggested un of
performance measures).

For those indies as vella ll of the other process measures described in part Baf ts section tobe
tffectively use tbe CONDITIONS and ASSUMPTIONS which surround them must be understood.
‘hese conditions andassumptionsare nat met, the measures wil have lite or no meaning and thes
9 value to understanding the processes rom which they were generated. Following are the fur mini.
‘mum conditions which mist D is foral of he capability mencures atar described in Part Bot

The process rom which the data come is statistically stable
© Tho individual measurement from the proces data form an approximately normal distribucion.
© The specications are based on customer requirements

There nistsawilingnessto accept the computed index (ratio) values tbe true" index (rio)
value=, to discount sampling variations influence on the computed number eg. a computed
ea of 1.05 may be fom a process whose true” Cy 140, views due simply to sampling.
‘vation, Please see Appendix H, References 19,3, and 2 for more on this subject.

ae

Y EN <p

D
Section 5. Understanding Capahiiy (Cont) - Suggested Use of Process Measures

al UT creme
E Ih All.

-@-

—__——— @ EM 6

4. CONTROL CHARTS FOR VARIABLES
Section 5. Understanding Capabi (Cont)

0.

‘SUGGESTED USE OF PROCESS MEASURES.

"he key to effective use of any process measure continuos o be the level of understanding o what the
‘measure truly represents. Those inthe statistical community who generally oppose how Cy numbers,
for instamer are being use are quick to point ut ha few rel world” processes completly at al
Ole conditions assumptions and parameters within which Cy, has been developed (see Appendix,
Reference Land Reference 18), Further, tische position of thi manval that, even when ll conditions
ree, its ul toasts or tray understand a process onthe basis ofa ingle index or ratio aum-
en for reasons discussed in te paragraphs below.

DA. The Loss Function Concept

‘The driving force behind how capability indices and other process measures) have been used has
‘been the understandable desire to produce all pars within engineering specifications. The under.
ing concep serving a the motivation for this desires the mentality thal parts within spe
ation, regardless of whore they are located or positioned within the speiintion rang, are
“good! (oracceptblo and al pars beyond specications, egurdles of how fa beyond specific:
tions they may De, are “had” (or unacceptable. Quality profesional sometimes reer o this cou
sept as “Goal Post” mentality oe Figure 29 (a)

Although this mental model (no ad) has been extensively usedin the past, it is suggeted that
‘more useful mode, one that alot loser tothe behavior ofthe real world, is the one pleted
in Figure 29. This model ake, in general, ho form ofa parabola and utes the principle that
a increasing quadratic (as oppose to ina loss incurred hy the customer and/or society the
further à parus characteristic gts fom the specification target. Implcit in this concep, r=
ferred to asthe loss funtion concept isthe presumption that the design intent peiiation tar.
ged is reasonably well aligned with the customer‘ requirement.

-8-

1. CONTROL CHARTS FOR VARIABLES
Section 5. Understanding Capabity (Cont) - Suggested Use of Process Measures

ae 4 om

E

+ sss oymswrna cree

Hl en coca

STA TIO mure oss PROCESS MU

3

Figure 20. Process Alignment to Requirements

-#-

CONTROL CHARTS FOR VARIABLES

Section 5. Understanding Capabliy (Cont) - Suggested Use of Process Measures
D2. Aligament of Process to Customer Requirements.

{Section Zof Chapter La process was depicted graphically (ee Figure, page). An output char
acteristic of such process can also be expressed graphical in tera of distribution of evar
‘ation. This distribution might be referred to as the process distribution tee Figure 80 (a).

‘loss function such as the one depicted in Figure 30(b) can bo ertablshed forthe proces chart
rite whose distribution is indicated in Figure 30 (a. Farther, assuming litle or no variation ln
the customer roqirement (specification tage, by superimposing the process distribution ento
‘the customer requirement los function curve (Figure 30 0), two observations can be made:

© Imorder to minimie customer loses, it is desirable 1 align the process (process center with
‘the customer requirement special tare

‘Tes additional beneficial tothe customer ifvaration around the target value is continually
rec (se Figure 90 (a)

This analysis sometimes called aligning the “Voice of the Process" with th “Voie ho Cu
tomer" (ste Appendix H, Reference 2, fr more deta shouldbe tod that albo no var
ation i assumed in the "Voice ofthe Customer” fr this example the “Voice of the Customer”
(specification target) does vary in the real word and this further complicates achieving tree
tomer satisfaction wth given proces

Final, when an estate translated os is generated by considering the actual distribution of
parts being produced by this proces, in conjunction wich the les being generated hy this proces,
can be shown at this case approximately only 48% ofthe totaler customer being
Account for by the parts beyond specification, while the remaining loss is coming rom parte
‘within speciation bat not at the target Figure 0 (9). This troy suet thatthe “Goal
oF computing percentage of “Bad” parts (parts beyond speiatons)in and of

itself doesnot provide a proper appreciation for understanding te elect the process ls actual
having on the customer.

&

Section 5. Understanding Capabity (Cont) - Suggested Use of Process Measures
DS. Applications of Process Mearures

Forreason discussed inthe forgoing paragraph and assuming the conditions listed in par Cot
‘this section have been met, he following is suggested relative to using process measures for en
Tnnood understanding and effective continual improvement of processes:

© No single index or ratio shoud bo uted to describe a proces; further,

+ Twoormorvindicosorraios should be viewed collectively — Ata minimum, the combination
(Of Cy and Cu, P ad Pa CR and Ca or PR and Fo for example, shouldbe used; end

(© is stanly recommended that graphical analyses be usd in conuneton with the process
measures Examples of soc analyses include contra charts, pot estimated proces dst
Bacon, toss function analysis graphs such a those shown in Figur 30, ete Additonal, pare
‘ela for unstable processes, migh be helpful to also graph or pot inherent proces var.
tion versus otal proces variation and/or dx, versus sto gun an appreciation fora rough
perception af the ap between the proces "apabliy” and "performance" and to track i
rovement Generally, ib ae ofthis gap a measure of the degre o which tho proces isout
‘ot contro, even though in unstale processes, depending onthe degree of instability, theres
‘respectively more variability and uncertainty in the process estimates (a, and 6,) than or
‘Sable processes Thso types of graphical analyses should be done for better process under
standing even if process measures (Le, C/ Cy, ete) are not computed and/or use.

+ Forcontinual procts improvement, process measure shouldbe wed with thomindstofcon-
{Unully attempting to match the "Voice of th Process” tothe "Voice ofthe Customer, with
‘nim Tos othe customer,

A final precaution is that ll opabiit assessments shoud be confined to a single process charac.
teristic Tess nove appropriate to combine or average Ue capable results or several processes
into one index

Hopeful, the application of process measures within this otal framework will provide somo of
the information necessary Yor achieving true process improvement a a competitive rate.

O EN

Basul tom Comparing the Process Outcome to an Accapionce Specification and
Deciging iit Conforms or Ross Nat Conform

People | | Equoment | | environment
Outcome is Classified
Conforms:
> “ACCEPT
Does Not Conform:
“REJECT
Manode
‘Outcome Examples Control Charts

Vehicle does not leak! looks

Lamp lights/ does not ight

+ Hole diameter undersized or oversized
{go/no-go gage)

+ Shipment to dealer correct or incorrect

+ p Chan tor Proportion
of Units Noncontorming

+ np Chart for Number of
Units Noncontorming

‘Bubbles Ta a windshield
+ Paint imperfections on door
+ Enors on an invoice

= € Cat for Number of
Nonconformiles per
Inspection Unit

‘© u Char for Number of
Nonconformites per
Inspection Uni

"The conformance criteria must be clearly defined and the procedures for deciding I
these ctra are mot must produce consistent results over te.

‘Acceptance Specification Examples

‘Comment

© Surface should bo free Wom Faw

+ Surface should conform to master
standard in color texture, brightness
and impertecions.

+ Any material applied to minor back to
prevent scattering shal not causo
visible staining of mirror backing

> What a aw?
=" Do inspectors agree?
= How measured?

+ Conform to what degroe?|

+ How measured?
+ Visible to whom?

+ Under what conditions?

Figure 31. Atributo Data

#-

GO E Y

Chapter III
CONTROL CHARTS FOR ATTRIBUTES

Although control charts are most often thought in terms of variables as shown in Chapter ID, versions
have alo been developed for attributes. (Ss Figure 31.) Atributo data have only two values conforming!
‘nonconforming, passa, o/no-go, presentabxen) but they can be sound or recording nd analyse"
Examples include the presence oa required label, th continue aan electa ica, or errors ina typed
document. Other examples are of characteristics hat are measurabl, but where the results are record in
‘simple yes/n fashion, such she conformance of shaR diameter hen measured on ago no-ko page the
‘acceptability of door margins toa visual or gage check, or on-time delivery performance, Control charts fr
tribute ao important for several sons

+ Attribute data situations exis in any technical or administrative proces, so attribute analyse tech
ques are useful in many applications. The mos significan dica ito develop preciso operations]
définitions of what is nonconforming

‘© Atribute data are already available in many situations — wherever there are existing inspections,
‘writeups for repair, sorts ejected materia, ee. In these cases, no addon data collection expenses
Involved, jst te effort of converting the data to contre car form.

‘+ Where new data must bo collected, attribute information i generally quick and inexpensive to obtain,
and with simple gaging (eg. a go/no-go gag) it ofen does not require specialized collection sil.

‘© Much data gathered for management summary reporting in attibute form and ean benefit from on
‘rol chart analysis, Examples inde department rat-ron OK paformancesraprates qual audit
and material jetons. Because ofthe ality to distinguish variation from special and common case,
‘contol chart analysis canbe valuable in interpreting these management reports.

+ When introducing contro charts into an organization, ii important to prioritize problem areas and
use charts where they aro most needed. Problem signals can come from the cst contol system, use
‘complaints, nternalbotlenecs, ete The use ofattbute contre charts on key overall quay moss
‘an often point the way ta the specific process areas that would nord more detailed examination = ne
lung the posible use of contre chart for variable,

‘This manual will use conforming/nonconforming throughout attribute discussions simply beacause

2) these are “traditional” used, 2) organizations ust starting on the path to contival improvement us:
lly egin with these categories and manyof the examples valable nature us these categories Tt
‘should not be construed that these are the only “acceptable” categories or that atributo charts cannot be
‘sed with ease 1 (se page 19 processes (ee Appendix HI.

‘The next four sections cover the fundamentals af four major types of tribute control chants

Section 1 = The p Chart for Proportion of Unis Nonconforming om samples not necessarily equal
ae

Section 2~ The mp Chart for Number of Units Nonconforming rom samples of equal sie)
Section 8 - The e Chart for Number of Nonconformities (rm samples of equal size)

Section 4 = The u Chart for Number of Nonconformities per Unit om samples not necessarily of
equal size)

‘The frst discusion, ofthe p chart, lengthier than the others, as ¿introduces the major concepts The
‘other three sections concentrate onthe distingushing features ofthese types of chart

Y E ee

PREPARATION FOR USE OF CONTROL CHARTS

Establish an environment suitable for action
Define the process

Determine characteristics to be managed
Considerations:
~ The customer's needs
= Current and potential problem areas
= Correlation between characteristics
Operationally define the measurement system

Minimize unnecessary variation

-9-

O En
M. CONTROL CHARTS FOR ARIES

Section 1
THE p CHART FOR PROPORTION NONCONFORMING

‘The p chart mensues the proportion of nonconforming (diserepot or so-called defective) tems ina group
items beng inspected. This could refor toa sample of 75 pecs, taken bios a day, some percentage of
production grouped on an hourly or daly basis, proportion an im deliveries, te. his may be based on
‘evaluating on characteristic (was a particular part instalo) many charset (vas anything fund
‘wrung atthe electrical str check station? e is important that

‘© Each component, part, oritem being checked is recorded as either conforming or nonconforming (even
‚fan item has several Spec nonconformities, e on tallied once as «nonconforming tem)

© The results of these inspections are grouped ona meaningful bass, nd the nonconforming items are
‘expressed asa decimal recon ofthe subgroup size

Before ap chart can be used, several preparatory steps must be taken:

+ Establish an environment suitable fr action. Any statistical method wil fil unless management has
prepared a responsive environment.

‘+ Define the process. he process must ho understod in terms ofits relationship o other operations
ers ad in terms of the process element people, equipment material, methods and environment that
alec it at each stage Techniques such asthe cause-and-elletdisgram help make these relationships
visible

‘+ Determine characteristics tobe managed. Concentrate on those characteristics that re os promising
for proces improvement (an pplication ofthe Pareto principe). Several considerations are appropr

= Ta customer’ neds. This includes both any subsequent processes hat use the product o service
asa input and the fra end em customer

— Current ani potential problem areas. Consider existing evidence of waste or poor performance (og.
Scrap, rework, excessive averti, missed targets) and arts of ik (e, upcoming changes 0
‘esi of the product or service, to any elements ofthe proce),

~ Correlation between characteristics. Foran efficent and efetie study, take advantage of elation
ships among characteris, If several individual chareteristies on an em tend to vary together,
may be slicen to chart only one of them (see Warning on page 29),

‘Define the measurement system. The characteristic must be operationally defined o that findings on
‘becommunicated tall concernedin ways that hav the same meaning today a yesterday. This involves
spring what information sto be gathered, where how, and under what conditions, Evtablishing op
‘rational definitions cn bo especialy fie bat spec important when personal jest
is involved The finition a the characteristic wl affect the type o contol dart tobe ua ana
Atibutes data chart ike the p chart, or variables data chart, as described in Section I

© Minimize unnecessary variation. Unnecessary external causes of variation should bo reduce before the
study begin, The purpose so avid obvious problems that cold and should be corrected even without
‘use of control charts tna cases, process log shouldbe hept noting al relevant events Sus proces
Aural changes, new raw material los, te. This wl id in subsequent problem analy

ao

HURT Fon ATTMGUTE D474 "mem STUDY

E |e
“Fou CTO TEST
aa ra Bh
0 ee EL
” Seat.
” sepas]
m
s rao
5
a
= E
eS
: =

aaa add lalalala

N em [relie fre | 13] [as 18 17 [re [is [ae [us [ar [ns [ho 16] 17 |20} 15] | ve [07 [10
Er ¡A ¡ARANA AAA]

= DRE oolala[: 2 le sl llo

pr

Figure 22. p Char for Proportion Nonconforming - Gathering Data

e

O E

IM. CONTROL CHARTS FOR ATTRIBUTES.

Section 1

1 Charts (Cont)

A. GATHER DATA

Aa.

Select the Size, Frequency and Number of Subgroups (See Figure 32.)

Subgroup Size— Charts fr attribute generally require quitelarge subgroup sizes te. 5010
200 or more) tobe ale to detec moderate shifts in performance: Fo the chart to show ana
‘yzable patterns, the subgroup sie should be largo enough to ave several nonconforming
items per subgroup (eg, nB> 5). Note, however, that argesubgroupsizs can bee disdvanı
{age if each subgroup represents a long period of process operation, Its most convenient if
‘subgroup sites ar constant orf they vary by no moro than 25%, but thls ned ot be th
‘xs. Itisalso help hat the subgroupsize be large enough relative to to generate lower
‘control limit hat assignable causes due to improvement may also be noticed,

D. Sudgroup Frequency — The subgrouping frequency should make sense in terms of produc.
‘ion periods toa in analysis and correction of problems found. Short ie intervals allow
{aster feedback, but may conc with requirements fr large subgroup sis,

© Number of Subgroups — The data collection period shoud be long enough to capture al the
likely sources of variation acting the process, Generally it should also include 28 or more
subgroups to givea good est for stably and stable, a reliable estimate of process perform

Aa.

"The following data shouldbe recorded fr sach subgroup:

‘The numberof items inspected ~n
‘The number of nonconforming tems found =p

From these, calelate the proportion nonconforming:

‘These data shouldbe recorded ona data form asthe basis of initia analysis, When the mest recent
Distorcal data are available, hey may be used to accelerate this phase f the stud.

Select Seales for the Control Chart (See Figure $2.)

‘Thechart on which he dataare plotted shouldbe ai outwith he proportion (or percent noncon-
forming as the vertical sal, and the subgroup identieation Ohr, dy, te) ke the horizontal
sale The serial scale should extend from zero to about 1-12 03 mes the highest proportion
‘onconforming noted inthe nial dita readings,

1. Plot the Proportion Nonconforming on the Control Chart (See Figure 92)

Plot the values op fr each sibgroup. Js usualy heat connect the points with nes to help
suai pattern and trends

AS the points ae plotted, rely san them to sei they are reasonable any pints are substan
tilly higher or lower han the others, confirm Chat the cautions are corea.

Record changes in the process or unusual oocurren
observed, in the “comments section ofthe cart.

estat may at the proces, a ay ae

-9-

LOL CHART FOR ATTRIBUTE DATA

EN

e

err)

VE 0828 + 0287 = 0581

ep 2 uct = aa VE
tee à 0237 = or

os fa fe or re

AAA

labre sel ee

RS SO EE

On POWER NTERRUPTOW

Figure 22, p Chart for Proportion Nonconforming - Calculating Control Lis, Sheet +

O E

A. CONTROL CHARTS FOR ATTRIBUTES
Section 1. p.charis (Cont

B. CALCULATE CONTROL LIMITS

BA. Caleulate the Process Average Proportion Nonconforming (5) (See Figure 38,

Pa.

Sheet 1)
Por the study period ok subgroups, calelae the average proportion nonconforming

men

whore mops map any ns. are the number of nonconforming tems and number of tems in-
¿pete ach ben Cre bulb take ot tone presage p10 with rope
ton defective (p-

Calculate the Upper and Lower Control Limits (UCL, LCL) (See Figure 39, Sheet 1.)
‘Th contro limits are the process average plus o minus an allowance for the variation tat could

boexpectedifthe process werein stats contol, gventhe subgroup sample iz. Por the stay
period ok subgroup, calculate the upper and lower contol nis

VL „ep 3 Ds
Leh, = p- 3, my

here nis he constant sample size
Note: Wen slow and/or a is small, he LCL can sometimes be alulated aa negative ue
era these cases theres no lower control imi sine even aval ofp ~ Dora particular period
‘Sith the limits of random variation,

Draw and Label Lines (See Figure 88, Sheet 1)

© Process Average () — soi horizontal ine

© Control Limits (UCL, LCL) ~ dashed horizontal ines

During the initial study phase, these are considered til contro init

052

Y E >

TROL CHART FOR ATTRIBUTE DATA

ES 28 :H ES

30x ISPECTONRIECTONS-Y00S

Lot em us pes
pe 7 FEST Day PRODUC

0

TES 01 Fe SEES 18
PGL LG = 01223 vores seu /T10 «0124 2270488 = 0122 2005» 015, 0098
THESE UNITS ARE FOR SAMPLE SIZES 1106 420% 9670 1488

1-2 URL LOL = 0122 327 VB 012.018 023, 2005.22 0122 27/52 012.018 028 —|
2.5 aids aan RT» on «ara 010. 041.210.0184 Aa VERE» Dl 0088 = 188. 0:
Bei. MR IN > 22 DNS 008 =

E BEE E

so

so

on
8

Ta

Men [o 1313] 1:15] tr os ls fr [14 [vo Jrs eo sos

=

a8

a

=

[os

ler Jas as lr seo] Le fo «| Le Le ro res |r} vo fr fox

E ELO ENTER BESTE

E

Figure 33. p Char tor Proportion Nonconforming - Calculating Control Limit, Sheet 2

Al. CONTROL CHARTS FOR ATTRIBUTES

Section 1

2 Charts (Cont)

NOTE: The control limi calculations given above are appropriate when te subgroup sizes
a all equal as they would bein a controlled sampling stanton). Theoretical,
henever the sample ie changes (even fr a single subgrou), the control its
Change, and unique limit would be enulated for each group having» unique
sample sie. However, for practical purposes, contol mits cleulated witha
vera sample size (8) are acceptable when the individual eubgroup sizes vary
from the average by no more han pis or minus 25% (pial octal production
volumes under relatively Sable conditions). For these sitios,

EL, LCL, =p + 3 {BC IR. When subgroup sizes vary by more than this
amount, separate control limits are required forthe periods with particular small
rango samples. reasonable procedure (which shouldbe documented in the
comments” section of the form) i

+ Determine the angeof sample ste that would vary from the average hy pls and minus 25%;
identify all subgroup wih sample size hat ie outside this range

(© Recalculate the precise limits fr those points a fellows:

VE, LOL, 264 3/PT= ep 2 ap BTR

‘were nis the sample size of the particular subgroup, Only the m term changes from point to
point

‘Plot the new upper and lower limits onthe chart so Figure 8, Sheet 2) forthe affected su
Aroups and use athe basi orienting spec cause

[Note that any procedure fr handling variable control limits i going to be cumbersome and may
Teud potential contsionamong people trying interpret the charts. Ls much botes here
sible to structure the data election plan so that constant sample ses can be sed.

CA

nd

==

salat sR ee Re

18)
El El

Figure 24, p Char for Proportion Nonconforming - Points Beyond Control Limits

0

DEE

A. CONTROL CHARTS FOR ATTRIBUTES:

Section 1.2 Charts (Cont

©. INTERPRET THE CHART FOR PROCESS CONTROL,

Objective: identity any evidence thatthe proces is no longer operating a the same level — that itis out of
control ~ and to take appropriate action. Points beyond control nits, or obvious trends or patterns nthe
data beyond what would likely orcur due to chance, suggest the presence of special causes of aration

Cil. Analyze the Data Plots for Evidence of Instability

Points Beyond the Control Limit (See Fire 34) — The presence ofone or more ponte e
‘yond ether control mit evidence of instability that point. Since ponts Deyo the com
{tol limits would be very rare if tie proces were stable and only eommon-cause aration
were preset, we presume that a special cause has accounted fr the extreme value The so:
‘cal cause may be her unfavorable or fvorable either station bars immediate invest
tion. This ste primary decision rule or action on any contre chart. Any point beyond he
‘contol limits should be marked,

point above theupper cotrallini (higher proportion nonconforming) s generally io
one or mere of the following:

© The control limi or plot point are in error
The proces performance has worsened, either at hat point in ine or spart oa rend,
© The evaluation system has changed (eg, inspector, gage).

A point bow the ower control limit lower proportion nonconforming i generally sign of
fone of more of tie following:

© The control iit or plot point are in error
‘The process performance has improved (this shouldbe studied fr improvements that

might be incorporate ona permanent bai).

+ The measurement sytem has changed.

Patterns or Trends Within the Control Limits — The presence ofunusual patterns ortrende
‘ren whenall points are within the control limits, can b evidence ol noncontrolor change in
level of performance during the period af the pattern o trend, Thi ean give advance warning
conditions which lef uncorrected, could cause pots beyond the contra limits.

NOTE: When the average number of nonconforming items per subgroup (09) 5 moderately
lange ( or more) the distribution of the subgroup pss nearly normal and trend.
analysis similar to that used for X charts can be used. When Becomes sal (6
bor fewer the following vues are not directly applicable,

oS ep ——————

+
A
he
! EEE)

Figure 35. p Char for Proportion Noncontorming — Runs

-100-

Sp EN

I. CONTROL CHARTS FOR ATTRIBUTES

Section 1

»

B.Charts (Cont - interpret or Contot

‘Runs (Sen Figure 85) — In a process under control, with 15 moderately large, approi-
‘ately equal numbers of points sould fall on either sido of the average Esther ofthe flow.
ing could bea sig that a process shit or trend has beg:

1 point ina row on on side af he average,

7 points in a row that are consistent increasing (qua or greater than the preceding
points) or consistently deerensing

In hese cases, the point hat prompts the decision shouldbe marked (eg. the seventh point
above the average: it may be helpful to extend a reference line back tothe begining the
run The analysis should consider he approximate inet which t appears that the tend ot
hi fat begun.

ans above the process average, r runs up, generally signify one or both ofthe following:

© The process performance has worsened — and may still be worsening.
+ The evaluation system has changed

uns below the proces average, or runs down, generally sity one or both ofthe following:

(© The process performance has improved (the causes should be studio for permanent in
corporation.
© The evaluation system has changed.

NOTE: When np is small (below), the likelihood of runs below $ increase, 5 nun
length of 8 or more could be necessary to senal a creme nthe proportion
noneoeforming,

Ce

a

AAA
+

= =f
SA

= E

Ñ
= E
om Tela Lu fil fess laff] 2 Lo Jes oso

Figure 36, p Chart for Proportion Nonconforming — Nonrandom Patterns

-102-

A. CONTROL CHARTS FOR ATTRIBUTES
Section 1. p Chart (Cont) interpret for Control

Obvious Nonrandom Patterns (Seo Figure 38) — Other distinct patterns may indicate the
presence of special uses of variation although care mst be taken not to ove-nterpre he
data. Among these patterns are trend, cycles, unurual spread of points within the control
limits, nd relationships among values within subgroups eg. fall nonconforming es cc
‘urwithin the firs few readings taken for the subgroup) One es for nal spreads pre
low:

Distance ol points rom the process average Generali a process under statistical con
trol, with only common-canse variation present and a moderately lege, about 2/9 of the
ata points wil be within the middle third of the gion between the control lit; about 10
‘of the points willbe inthe outer two-thirds ofthe reson about 120 wie relative ose to
‘he contol limits Gn the outer third ofthe region)

substantially more than 2/3 ofthe points ie close tothe process average fo 25 subgroupsit
‘over 90% arewithin themida third of the control imi eon), this cou ean one or more
tthe following

‘The control ints o plot points have been miscalculate or mispotod

© The process or the sampling method are stratified each subgroup ytematially contains
measurements from two of mare process streams that have very different average por.
formance (eg, the mixed output of two parle production ines).

‘+ The data have Deen edited (ales that woul have deviated much from the average have
een ered or removed,

substantially fewer than 2 ofthe pots Le lee to te proces average for 25 subgroups
40% or fewer ar in the mide thd, this could mean ane or both ofthe following

{Caution or loting errors have been made,
© The process orth samplingmethod ene sucessve subgroups to contain measurements

ftom wo or more process treams that have very dierent average performance eg. per
formance dferenees between shift)

IE severa process streams ae present, they should e iento and tracked separately

-109-

8
a :B
mx NAL FUNCTIONAL TEST
mont, aa a =
» ee
Py ==
0
a
E
a
4s
o
PRE
e
o
Im
fl we reis ss [15] 0 | 25] 10] 7 [sis [os fos | at 16] 10] 16] 17 a0 iso
Ur | ¡AAA
jur
Jolla [rio bs ello] Le Lo LL Le

ER

Lee

Figure 37. p Char tor Proportion Nonconforming — Control Lits Recalculation

040

I. CONTROL CHARTS FOR ATTRIBUTES

Section 1. p Char (Cont) - interpret tor Control

ca,

cs.

Notes

ind and Correct Special Causes (See

Wen an out-of-control condition has ben ¿dente in the data, the operation of the process
ust be studied to determine the cause. Ti cause must then be corrected an tothe extent pos
‘ie, prevented from recurring. Since special cause was indicate by the control hare nalts or
‘he perationsiscaled for, and one would often expect o ind eases of variation within the aby
ofthe operator o local supervision to corret Problem solving techniques suchas Preto nalga
and cause-and-effect analysis can be helpful (se Appendix, Reference 11),

For ongoing studies being made with real-time data, analysis af out-of-control conditions in-
volves the timely investigation of the operation of the process, vih emphasis om finding what it
any, changes occurred that might explain the abnarmal performance. When this anal has re
ult in corrective ation, the effetiveness ofthe action should become apparent nthe cota)
an.

For preliminary studies with historical dat, the passage of time may make analysis of process
operating changes moze dificult, especially for symptoms that come and go The analysis must be
sae as well as poste under the circumstances, to identify the condition and to prevent tse
rence. A wel documented “comments” setion could be Very bela inthis regard

Recalculate Control Limits (See Figure 27)

Wien conductingan ntl process study or areasessment ofthe process capability, the tril on
tro iit may need to bo recalculated to exclude th elit of periods whe state o control was
affected by special causes which have been corrctd, The contol lts should he recleuated
‘excluding the points associated wit the special cause an pated on the chart per paragraph Bat
this section. This sep prevents abnorma] production periods for being included athe mate
pl variability The historical data should again be checked against the revised limits to con.
firm that no further points suggest the presence of assignable cases,

Once the historica data show consistent performance within the tral control init the limits ean
Ve extended forward to over future periods. They become the operating contr lite against
hich the future data wil be evaluated a is gathered and recordad,

‘The limits for ongoing contol may be tere fom those developed during the analysis period by
‘hanging the sample size. In such a ease, te Basic forms fom paragraphs Bl. and B2 are
se, ut wth the desired sample size any instead of 5

For more extensive discussions of interpretation, tests for randomness In data, and
problem solving, se Appendix H, References 6 through 12,

-105-

From the example:

B

0812

Process capabiliy current is 3.12% falures of the functional
check (96.88% OX),

EVALUATE THE PROCESS CAPABILITY

If the functional check is performed 100% and nonconform-
ing products are set aside, the customer Is being protected
{rom receiving nonconforming product, but the 3% average
{allure rate (requiring rework or scrap) is wasteful. Actions to

CALCULATE THE PROCESS CAPABILITY
| improve the chronic performance level should be developed.

= 106-

I. CONTROL CHARTS FOR ATTRIBUTES
Section 1. 2 Chars (Cont

D. INTERPRET FOR PROCESS CAPABILITY

‘When contro issues have been resolved, (peral causes ented, analyzed and, where appropriate, cor
rected/prevoted from recurring) the control ehartrefeets the underlying process pub, For the p
‘hart (and al other atribute chart), process capability dos fom tha for variables data inthe sense that
ac pion anattribate chart direct indicats percent ar rate of product nonconforming out-of specif
‘ations 0 customer requirements, whereas points ona variable chart indicate what the proves syed,
irresperive of engineering specfations. Therefore, or attribute charts, cab e defined simply as the
Average proportion orate of nonconforming produc, whereas capability for vaeabes charts refers tothe
{ota inherent) variation (6 x yield y the (stable process, with and/or without adjustments or proc
centering to specification tarot.

DAL. Caleulate the Process Capability

+ Fora p chan, the process capability is refeted by the process average nonconforming, $
calculated when al points ae in control I desired, this cn bo expressed asthe proportion

conforaing to specification (1 -

+ Fora preliminary estimate of process capability, use historical dato, but exclde datapoints
associated with special eases,

+, Fora forma proces expability study, new data should bern, preferably for 25 or more pen

(ds, with the points al rfetng statistical control. The 5 for these consecutive contr!
periods i better estimate ofthe process current copay

Da. Evaluate the Process Capability

‘Tho process capability as Just alulated ect the ongoing level of performance thatthe
roots is gonerating and can be expected to generate, a Jon as the proces reais in Co
ol and does nt experince any basic change performance. Ona periodto- period basis
he measured proportion nonconforming will vay between the control limits, but barrio any
changes in the process o pesiads allowed to go out of control, theaverage proportion poso
forming wll tend vo be sable.

© This average capaiity, ot the Muctuating individual values, must be evaluated against man
arements expectations fr the particular charcteristc Then if thie average level mac.
pie. further analysis and action must he directed toward the process ac! (management
responsibil),

-107-

Y E >

IMPROVE THE PROCESS CAPABILITY

‘Toimprove the chronic performance ofthe process, concen-
trate on the common causes that affect all periods. These wil
Usually require management action.

CHART AND ANALYZE THE REVISED PROCESS

Confirm the effectiveness of system changes by continued
‘monitoring of the control chart.

= 108

O E iy

I. CONTROL CHARTS FOR ATTRIBUTES:
Section 1. p.Chans (Cont) - Interpret for Process Capabiy

D3. Improve the Process Capability

Once the proes is demonstrating statistical contol, the remaining average level of noncon+
formes will ect the systemate causes of variation the underlying process the prow
ss capablty, The types analysis performedin lagnosing the special ease (concaD io,
‘which focused on operations, wll no longer be appropriate in dlagnosig common cause af.
fecting the system. Unless management action directed toward the sytem cf no im

provement inthe process capability canbe expected, Long-term solution are necessary 10
Correct the soures of chronic onconforities,

Problem solving techniques such as Pareto analysis and cause-and-effect analysis can be
Bell (se Appendix, Reference 11), However understanding ofthe problems an be dil
cultwhen nly attributes data are wed. fa general, problem hi aided by ging upstream
inthe proces as far as possible toward the source of suspected causes of variation, and DY
‘using variables data for analysis (eg, in X and R charts)

DA. Chart and Analyze the Revised Process

©. When systematic proces actions have ben taken, hir effects should become apparent inthe
‘control char; the chat becomes a way of veryng the ofseiveness of the ation

(© As the process change i implemented, the control chart shouldbe monitored carefully. his
change period can be disruptive to operations, potential causing new contra problems that
could obscure the true effec of the sytem change,

(© Afterany special causes of variation hat appear during the change period have been denicd
“and corected the process vil ben statisti] control ata new proces average, This new a
trae reflecting in-control performance can be wd as the bass of ongoing process conta
However, investigation and improvement ofthe system should continue

-100-

E :B :B E
x ‘SPOTWELDS-UNDERSE

nos 40 we tae my Eee

2 = E
2 Y
=p le

mms [Y [2 fa | «(5 | 547 Ja [o Jo Jo re ra Jus o 17 re ro ao | o fo

jure 29. np Chant tr Number Nonconforming

-u0-

> 1

ll. CONTROL CHARTS FOR ATTRIBUTES:

Section 2
THE np CHART FOR NUMBER NONCONFORMING

‘Tho np chart (ee Figure 88) measures the number of nonconfarming (diserepat or ea detective)
items in an inspection lot ts dental to the p chart except tat the actual number of nonconforming
‘tems, rather than their proportion ofthe sample, recorded. Both pad np charts are opproprne fr the
ame basi situations, withthe choice going tothe np chart i (a) the actual number of noncontormties
more meaningful or simpler to report than the proportion, and @) th sample size remains constant fon
‘period to period. The details of instructions for the np chart are virally dential to those forthe p char
exception are noted below.

A. GATHER DATA
(See Section 1, Part A ofthis chapter: exceptions are noted below)
© Theinspction sample size must he equal. Th periodo! subgrouping should make sense in terms
production intervals and feedback systems, and samples should e large enough to allow severe
nonconforming items to appear in each subgroup. Record the sample size 0 the frm,

© Record and plot the number nonconforming in each subgroup (ap).
B. CALCULATE CONTROL LIMITS
(Gee Section 1, Part B ofthis chapter exceptions are noted below)

+ Cateuat the Process Average Number Nonconformin (5).
ENEE
hese op, np … are the number nonconforming in each of hol subgroups.

‘Calculate the Upper and Lower Contra Limits (UCL, LCL).

PTE En)

retocar fora BY 000}

where n

the subgroup sample ie

©. INTERPRET FOR PROCESS CONTROL

(See Section 1, Part C ofthis chapter)

D. INTERPRET FOR PROCESS CAPABILITY
(See Setion 1, Part D ofthis chapter). Note the proces capability for an mp chat Ist justas itis

fora phat

-m-

va

CONTROL CHART FOR ATTRIBUTE DATA

x 38:8 E
xx SAL NSPECTON AS BENG CUT-LAWSPER BOLT

= aa

" +

2

+ |!

Hi} ‘worm aji jmJejrJ0)s ira] 7 folie] 4 Is 17 ja 1313 1512]? felt Is le

Ir

=: lr lalslelsfrlolofolololols libelo lo foo ls le ls [5 12 da

PEN ECTS Her WU Fo Te oe PES AE OM

Figure 39. 6 Char for Number of Nencontormiies

ue

I. CONTROL CHARTS FOR ATTRIBUTES

Section 3
THE © CHART FOR NUMBER OF NONCONFORMITIES

‚The chart (see Figure 89 measures the number of nonconformities (Biserepancies o so-called defects) in
an inspection lot (as oppsed tothe namberof nis fond nonconformig, a plotted onan np chard) Thee
‘chart requires a constant sample siz o amount of material inspected eis applied in two major pes of
Inspection situations

‘Where the nonconformites are scattered through a continuous flow o product (ng, as ina ol of
vinyl bubbles in las, or spas of thin Insuaton on wire), and where the average ae fonc on
ties can be expressed (eg, Das per 100 square maters af in).

Wheto the sonconformities from many different potential sources may be found in a single inspection
luni eg. the writeups at a departmental repair station, where each individual vice or component
‘could have one or more ofa wide varity of potential mnconformiis),

‘The following are the steps in construction and application of ac chat, which are similar to the basi ap
proach described previously frp chart; exceptions are noted below:

A. GATHER DATA

(See Section 1, Part A ofthis chapter exceptions are noted below)
‘Theinspecton sample sizes (number units, are of fabri, length of wire et) ned tobe equa so that
the ploted values fe wilreñec changes in quality performance rate of occurence ofsonconformitis,
© rather than changes in exporure the same size). Record the sample size on ih form

Record and plot the number of nonconfarmites in each subgroup (6.

. CALCULATE CONTROL LIMITS

(See Section 1, Part B ofthis chapter exceptions are noted below)
Cleat the Process Average Number of Noneonformitis (€ }
ER
‘where €, 6 ar the numberof nonconformites in ach ofthe k subgroups.
Calculate the Control Limits (UCL, and LCL.)
User
LOL ee ae

INTERPRET FOR PROCESS CONTROL
(See Section 1, Part C ofthis chapter)

). INTERPRET FOR PROCESS CAPABILITY

(Gee Section 1, Part D o thi chapter: exceptions are noted Below)

‘The proces capability s ©, the average number of nonconormiis in a sample of fixed size.

-ns-

wa

‘CHART FOR ATTRIBUTE DA

‘one :B 8 xa

‘ac-auor | BOOK AUDT- ALL DEFECTS

PP pe
so 2 Fra pena

VE rs gr ao |

40

30

20

De

sop Islefslalslzlzlalafalzlalale

gee Ttoıkohsksliarlahafzıhshsheß«!

| = | Jyr)ro [rs] of Jue) asf a
ee

om [so os [e rs re fo fo ffs [as

SANDER mores RE OS CORRE on PROCESS MENDIGO ACTON

Figure 40. u Cher for Noncontormies Per Unit

ES

Section 4
THE u CHART FOR NONCONFORMITIES PER UNIT

The chart (see Figure 40) measures the number of ronconfommiis(iscrepancies or so-called defect) pes
inspection reporting unt in subgroups which can have varying sample ses or amounts of material I
pected, Is similar to the chart except thatthe number of nonconformitivs is expressed ona per Uni
ass Bath and e charts are appropriate forthe came basic data stations; however, thew chart may be
sed ifthe sample includes more than one “unt” (a make the reporting more meaning, nd i ust be
edit sample sie can vary from period to period. Thedetals instructions forthe chart ar sir to
‘those fr he p chart exceptions are nated below

A. GATHER DATA
(See Section 1, Part A ofthis chapter exceptions are noted below.)

‘+ Sample sizes do not need tobe constant from subgroup to subgroup, although maintaining them
‘within 25% above or below the average simple the caleta of contol limits

(© Record and plot the nonconformitis por unit in each subgroup (u:

‘where ci the number of nonconfrmities fund, and n isthe sample sie number of inspection
reporting unit) ofthe subgroup; cand a shoul also be recorded onthe frm.

NOTE: The sample size foreach subgroup, , i expressed in terms of inspection reporting
‘units. Sometimes the reporting units a single production un, eg. an engine, Olten,
however, the inspection reporting units other than one production unit For instance,
in reports shoving noncontormitts per 100 units, the reporting unit i 100 production
‘units, and n shows how many hundreds were inspected

B. CALCULATE CONTROL LIMITS
(See Section 1, Part B ofthis chapter exceptions are noted below)

‘+ Calculate the Process Average Nonconformities Per Unit (a)

where cz. and, n are (he number of nonconformiies and sample sie of ech ofthe sub»
groups
Caleae the Control Limits (UCL and LCL)

off

Leb. o- ME

where ms the average sample size

152

ox :8 :8 LS
x DOCK AUDI AL DEFECTS
PES cage Son 9 BOXES
so Fro Pea on
Mt VI Vine means ane =
Mu ae VE «Var circa
CRE EN ENCRES
” =
ie El
ED I D na Si
so
Pe:
10
re i Sie
2
swe lalelfejetr|7|s|s]e|7|s|2|e/e)e]«[s|:2lrelmle|s|a|s
#5 Te |7|r0]s5]25] © [19] freir o ns zero ses ss asa | fre
ogre hokıkohskshshalahskihshahszehshskshshshehehsls Pelıs!
vo | [rol [refs |i fs fs [261 1 2 | a | Lo ls ro ee fs
"SRDS PEORE MATERIE OUEN MECS PUE, COSTOS

Figure 41. u Chart Control Limits Recalculation

n6-

1. CONTROL CHARTS FOR ATTRIBUTES:
‘Section 4. U Chars (Cont) - Calculate Control Units

NOTE: (See Figure 41) Ifany individual subgroup sample size is more than 25% above or
‘below the average sample ie, recleulate te precio contol init as follow:

UCL» LOL ma 3/0//0= 5

where is the process average and ás the sample size (numberof inspection report
ing units) o the particular subgroup Change the limits on the chart and use asthe
asis for identifying special causes

‘Note that any us of variable contrl limits is cumbersome and potential confusng
‘eis much better wherever possible t avoid this situation y using constant sub
group ample ies,

©. INTERPRET FOR PROCESS CONTROL

(Gee Section 1, Par € ofthis chapter

D. INTERPRET FOR PROCESS CAPABILITY
(Gee Section 1, Part D of this chapter)

‘The process capability is. the average number of nonconformiies per reporting unit

ne

a
%

us

O E 90

Chapter IV
PROCESS MEASUREMENT SYSTEMS ANALYSIS

Section 1
INTRODUCTION

Once the characteristics) o be measured i determined fr a give process, an evaluation ofthe measure:
‘ment system for that characterisic) should be underalen to ensure elective analysis a an subsequent
‘SPC dita generated for that characteristics). Recall te fundamental finding shared by satsicins and
‘tality professional throughoot the word that an observed values composed ofa master value ofthe car
Aetritie being measured plas measurement error, oF

‘observed value = master value + measurement error

“Measurement error is statistical term meaning the net effec fal sources of measurement vribiity
(hat causean observed value to deviate from the master value Unfortunately, this rltion hip means wear
faced with making decisions abou produet using information Ge, numbers) Chat contains addtional an
ality. Crying his one stp further the total variably na set of data consisting of lest two mete.
‘ments pert (or subgroup) and many ats (eubgroups) overtime corresponding) composed otto cor
ponent parts, ie,

total variability = product variability + measurement varia”

‘Te importance of minimizing the effet of measurement varity on assessments o proces variability
cannot be overstated, Para more complete understanding ofthe various aspects ol the sujet of measure
ment ysters analysis, please refer tothe automativeindassy’s Measurement Sytem Analysis (ISA) man.
Appendix H, Reference 19) published in December, 1090, y the Automate Industry Acton Grocp
(IAG) Oneof the more straightforward and also widely applied methods of measurement systems mayan
presented inthe ASQC Automotive Divison AIAG MSA Manuals presented her in tis section asa Ye.
Souably well accepted approach for asessinga measurement system prio to enpapap in state! press
contol In no way iit meant to suggest that this ithe onl acorptabe MSA technique. Additionally the
technique presented here assumes the other key strbutes of a measurement system, Le, aura,
arity, and stability, as describe inthe MSA Manual, have been evaluated and dered acceptable

* Please soe Appendix H, Reference 36

us

L mt

IV. MEASUREMENT SYSTEMS ANALYSIS

Section 2
AVERAGE AND RANGE METHOD

The Average and Range method (X and R sometimes refered tos the “Lang Method”) ia mathematical
method which wl determine both repeatability and reproduit ora measurement syste, Tis method
vil low the measurement system t be decomposed ino two separate component, repeatablyan re
producti

A

repeatability is large compared to reproducibility, th reasons may be:
© The gage instrument needs maintenance

The gage shouldbe redesigned to be more rigid.

+ The damping or location for raging needs to be improved.

© There is exossvewithin-part variacion

IE reproduct is large compared to repeatability, then posible causes could be

+ The operator neds to be better trained in how to use and read the gag instrument.
+ Calbraion on the gage dial ae ot ela

A fit of some sort may be needed to help operator us the gage mare consistently.

CONDUCTING THE STUDY

Although the number of operators, trials and parts maybe varied, the subsequent discussion represents the
‘optimum conditions for conducting the stud: Refer tothe age Re daa sheet in Figure 42 on page 124
‘The detailed procedure es follows:

1. Refer to the operatorsas A,B, and C and number the part 1 through 1050 thatthe numbers are
ot viable othe operator.

NOTE: The ten part should be randomly selected across fll rango af the process itis
important that the parts, in as much ass posible be representative of he total
procs (ation,

Calibrate the e.

Let operator A measure 10 parts na random order and have another observer enter the results in
row Le operators Band measure the same 10 parts without seeing eachother’ readings, then
enter he resus in vows Gand 1, respectively.

4, Repeat the cycle usinga diferent random order of measurement, Eater data in rows 2,7 and 12,
Record the data in the appropriate column. For example the ist piece gaged is part 7 then ze
‘ord the result in the column labeled part 7. three ras are needed, repeat the oe and enter
‘ata in rows 3, Band 3.

5. Stops9.and 4 maybe changed tothe following when large pat size simultaneous unavailability
fof pars make I necessay

a. Letoperator measure thefirtpartandrecotd the reading in row, Lt operator Bmeasure

‘the fest part and record the reading in row 6 Let operator C measure the int part an
‘ord the reading in row 1

-ın-

Y EN <p

w.
Section 2. Average and Range Method (Cont) - Conducting ine Study

b. Let oprator A repeat reading on the frst par and record the reading in row 2 operator B
‘ecordtherepeatadinginrow and operator record the repeat reading ro 12 Repeat
this cle and enter the result in ows 9, Band 13 if three tial are tobe ch

8. Analternative method may be wsedifthe operators are on diferent shits. Let operator A measure
“10 parts and enter the readings in row Then ave operator A repeat the reading afferent
Orderand enter the results in rows Zand 3 De the same ith operator Band Con te other shi

B. CALCULATIONS.

‘The Gage Repestabilty and Reproducibility calculations are shown on Figure 42 and Figure 4, Figure 42
shows the datasheet on which al study results are recorded, Figure 43 displays a report sheet on whichal
dentiing informations tobe recorded andallealcuatons made according to the presrbed formula. The
procedure for doing the calculations ater dats ha been elle as follows:

‘Sobtract the smallest reading from tho largest reading rows 1,2 and; enter the result in row’.
Doth amer rows 6, Tand8;and D, 12and 1Sand enterresitsinvows and 15, respectively
igure D

2. Entries in rows 6, 10 and 15 are made us positivo values. (Figur 42)

Total row Sand vide the total the number of arts sampled to obtain the average range fr he
Sat operators trials R, Do the same for rows 10and 15 to obtain Ry and Fo. (Pure 42)

4. Transferthenverage oftows 5, 10and 5 RR, R;)torow)7, Add them togetheranddividey
{he number of operators and enter results a R (overall average rango. Figure 42)

5. Enter R (overage value) in rows 19 and 20 and mulply by D and D, respectively, o get the
lower and upper contra limits Note Di 2er and Ds 327 trial are used The al ofthe
Upper Control Limit (UCL) ofthe individual ranges i entered in row 19, The vale of Lower
Control Limit (LCE) for os than seven tris is equal to zer, (Figure 42)

6. Repeat any readings that produced a range greater than the alelated UCL using the same op-
‘erator and part as originally used, o discard thot values and re-aveage and recumpute R and
‘he limiting value UCL based upon the revised sample size. Correct the special case that pro
‘ced the oat of contol condition.

7. Sum the rows (rows 1,2, 8, 6,7, 8,11, 12, and 19), Died the sum in each row by the number of
Part sampled and enter these values inthe rightmost column labeled Average’ (Figure 4)

8. Adduheuveragesin rows 1,2and Sand divide the otal by the number o ras andenterthe value
in row din the X, lock Repeat this for rows6, 7 and and 11, ad 19, and enter the results
‘the blocks for X, and X, in rows 9 and 14 respectively. Figure 49)

9. Enterthe maximum and minimum average af ows 4, and Min the appropriate spaein row 18

and determine the differences. Enter ths diflerence inthe space beled Kur in row 18.
igure 2)

12.

IV. MEASURCMENT SYSTEMS ANALYSIS
Section 2. Average and Range Meihas (Cont) - Calulations

10, Sum themensurements foreach rial for each part, and divido the totaly the numberof measure.
ments (numberof tral times the numberof operators). Enter the results in row 16 a the spaces
provided or part average. (Figure 42)

11, Subtract che smallest pot average from the largest part average and enter the result inthe space
Inbeled R, in ow 16. Ry is the range of part averages. (Figure 42)

12, Transrthe calulte values of, Nop and tothe blanks provided an the report ide of the
fore Figure 43.

18, Perform the calelations under the column entitled “Measurement Unit Analysis” onthe lt ide
of the form. (Figure 43),

14. Perform the calculation under the column entitled“ Process Variation” on the right sde af the
form (gure 4.

15. Check th results to make sure no errors have been mado.

(©. ANALYSIS OF RESULTS

‘The Gage Repeatability and Roproduciiity Data Shoet and Report Form, Figure 42 and Figure 49, wllpro-
vide the method fr analysis of age study data. The analysis wl estimat the variation and percent of proc
‘essvariaton for he otal measurement system anditsamponentsrepesabilit, eproducbility, nd part
{to-patt variation. On the et side ofthe form (igure 43) under Measurement Unit Analysis, the 8.19 ane
dard deviation spread which consumes 99% ofthe area under the normal curvo i calelaed foreach compo:
nent of variation,

‘The repeatability o equipment variation (EV oe) i determined hy multiplying the overall average range
(RY by a constant (Ky depends upon the numberof trials used inthe pago study.

‘The reproducibility or appraiser variation (AV orc.) i determined by multiplying the maximum average

operator difference (Ku by a constant (Ko). Ke depends upon the numberof operators used inthe gage
‘uy. Since the appraiser variation is contaminated hy the equipment variation, must be adjusted y sub
racing fraction ofthe equipment variation, Therefore, the apraiser variation (AV) i cslxlted by

‘where = number of parts andr = number of tas. Ifa negative alu iscaealated under the square oot
Sign, the appraier variation (AV) default o sara (D,

Y EN E>

‘OPERATOR! PART
‘TRIAL# 1feTs[«[s[e[7] s] se]
Lat
jects =
“ac I! Ke
526, Re
Par
wc Ke

1086, Re
a
2 [Esa

Es

a

Re

Ro +R _1/I#OFOPERATORS

18 fete -Min C= Koa

1 (Re «Dee

(Re xDy= jc

SD, = 327 for2tiasand2.58for ral: D) = Oforupto tral. UCLarypresents the limi fimiviual
Ris Cree those that are beyond this mi. [doi he cause and correc opos these readings ung the
sameappraiserand ni a originally used o dead values and e-averogeandecompute Rand he nie
ing value fom the remaining observations,

Notes:

Figure 42. Gage Repeatability and Reproductbiny Data Sheet

ee

a

DER

Part No. and Name

Gage Name Date:
Characters: Gage No: Performed by:
Speatietin: Gage Type:

Prom datasheet: R = Kar = Re

Measurement Unit Analy

| Repeatability = Equipment Variation (EV)

IV E
apnea Teale [E
== 2 Jus
s | sos

Reproducibility Appraisr Variation (AV)

AY TOA AU

om

DAT ETS ETC") LAS
Man -—.
Mo
pale pe
. En
= E En
EEES
RER = JŒVI AVS % RAR = 100 R&RTV)
a 5 wu
a} Parts | Hr
L En 2 385 u
FEV PT 3 | am
PV = Rp x Ky 4 230 PY 100{PV/TV)
= 5 | 208 = 1000)
= s | is re
+ lie =
al Vara FH ls |
Wo | | Ae

autre a orn eran

sonne on Table Da “Qui Conta and ntl Staats” A. Dana Bee Aer Br

Figure 43, Gage Repeatabity and Reproducibility Report

125-

‘The measurement sytem variation for ropstability and reproducibility (RER or 0) is caleulte bya
ag the square ofthe equipment variation and the square of the spraier variation amd taking the square
eût as follows

R&R= ENT ANT

‘The part-to-prt vacation (PV or 0,) is determined by multiplying the range of part average (8) by a
constant (K). Ky depends upon the number o part ued in the gage study.

‘The total variation (TV or) Som the study is calculated hy summing the square ofboth the repeatability
and reproduciiity (RW variation and the part-to-part variation (PV) and taking the square rot asf.
tows

= RER ENT

Ihe process variation is know and its values based on Go, then can be used in place of the total study
variation (TV) eaeulated from the gage study data, This i accomplished by perforting the following tw
‘aleaations

Both of these values (TV and PV) would replace thse previously alle
‘Once the variability for each factor inthe page study determined, can be compared tothe total variation
(TO. This is accomplshed by performing the calculations on Ih right side of the page report form
(Figure 49 under "% Process Variation”

‘The percent that the equipment variation (% EV) consumes of the total variation (TV) is ealelated by 100

” ww m]
enen lt]

le]

‘The results ofthis percent proces variation shouldbe evaluated to determine ithe measurement systems
acceptable fort intended application,

-126

O Hz

IV. MEASUREMENT SYSTEMS ANALYSIS
‘Section 2. Average and Range Metnog (Cont) - Anayel of Resuits

Ifthe analysis based on percent of tolerance is preferred instead of percent of process variation, then the
‘ee repeatability and reproducibility repart form (Figure 49) an be odie sb thatthe ight had de ot
he form represents & of tolerance instead of % o procs variation. In that ease, % EV. € AV. RAR
and % PV are calculated by substtting the valu of tolerance nthe denominator ofthe cacultioasinelacs
‘of te total variation (TV). Both approaches should be taken,

Guidelines for acceptance of page repeatability and reproducibility (% RER) using both approaches de
scribed above ar

© Under 10% error = Gage system OK.

* 10% 40 20% error ~ Maybe acceptable based upon importance of application,
east of gg, cor of repels te,

+ Over 0% error = Gage system needs improvement, Make every effort to
‘Ment the problems and have them corrected.

D. EXAMPLE

‘The XYZ Corporations starting an evaluation of measurement systems. The fst measuring device tobe
aluated sa shot thickness pige. The Quality Engineer decided co use ten parts to represent th veria
‘ty ofthe process and thre randomly selected operators from the inspector pol. Since Lime war a con.
‚train, only two trials would be performed. The method of data collection and anal lows tho pro
dures discussed earlier in this sction with the rests shown on igure 44 and Figur 45.

‘The upper contsl init (UCL andthe lower contr limit (LCL forte individual ranges are calculated
as shown in Figure 44, The data could be plotted on a repeatability range control chart bat amis af the
rango indicate that all ranges are in contre (.e, between the UCLa and Let), This means al operators
are consistent and are sng the gage in (he same wy.

‘The measurement unit analysis and percent process variation for each component of variation must then be
‘lleaated (se Figure 45). Th results should be evaluated to determine ithe measurement gt le.
‘ceptable forts intended application In this example, ho & RER i 25.2% and therefore the mensuromest
system would be considered marginal for messurng the proces variation,

un

PART
OPERATOR! air
TRIAL. EU EA CO IC E CACA
aa 5 ass [100085 Joss Jass [100 Jans Joss | 1o0 |
222 [am | von lan | oms 045 | Lan Fan |
aT
save. [pos [100 [ass [oso [oso | 1.00

ano, loos logo 1005 [oso loxo Joon
SEI Joss Les [aan [oso [240 [Lo pes
pr a as sas o Pra |om ra [ar |om | am
9 ave. ss |100 [ore |ozs |oxo [1os [098 [ozs [os Joss |= om
1 ang, |o9o loue Loos Loos Joo 1005 ons [oos ons |o05 Im» ans
Cie os Paso EE [oso Los Jam | as”
ee | oss | 100 | o [oso [oso [1os [095 [oso [105 [os | nn
it
18 ave. Joss |108 [oso [950 Joss |108 [oos [oso [105 Joss [x= os
15. RN 205 005 loo |o.00 105 [ous loo Jam |ooo Re
16 PART

ave_œalosr |1or loso losa loss Ino2 loss loss 1101 loor [me 058
TVR 0.06» R = 0.0 + R= 0.031/(# OF OPERATORS = 3] + Re 006
18 [Max 083 Min X=0.77 1= Kar 006
19,_{ R=0.08 x De = 0.15 Je UCL, 019
20 0.08 x Dy* = 0.00 ]=1CL 000

21for2trialsond2.58for tals D) = OforuptoT trials. UCL represents thelimitofindvdeal

‘re Cire those hat re beyond thi it. dently ho cause ad correct. Repent hese readings using the
‘ame appraiser and unit asorginaly used or discard vauesandre-averageandrecompute andthe limit
{ng value from the remaining observations

Note

Figure 44, Gage Repostabity and Reproduciomly Data Sheet - Example

-198-

‘Chapter, Section 2

at Na an Name Gast Gone Dm Da ut
Bts ie gaa Le Fe
Be Te, SRR. SP ae
N Korn 2,2 088
me Prec Venton]
RE pm Var EI
E ser - men
Ta [| Be
a. re
i | is
RE Wan A ESOT
AV Ku Ko (EVE /nn)] ons
Ma “ss
(0.06% 2.70)*= (0.18710 x}
oe
Co Ema um
Re Helen
Tommi Roc WER
RER (Ga aman soin
RR Dark Tomas
an
zo DE
Van 3 | as
Pos 2 (32 eer
= 0.56 x 162 p 2” = 100 (0.90/0.93)
a sis Le
mors | |

= 026050

SAS where del miens ne

‘heres pentes on he sae lor al 2d ese te ely an on
ee
id tom ae D "Qu Cora Ina Say” Ad, Dotan, ee han tee D

iyo ange eon

Figure 45, Gage Repoatabiny and Reproduciomty Report - Example

ne

sa

-100-

O a

APPENDIX A
Some Comments on Subgrouping

(Control charts are used to answer questions about a process. Inorder to have a control chart be weit
is important that the charts answer the right questions. An X-bar chart asks the question, Is the var
ation presen in subgroup averages mare Un e expected based on the variation within subgroup"
‘Therefore, understandingsoures of variation within and between subgroupsisof Paramount impar
tance in understanding he control chart andthe process aration. Most variables contol charts com
pare within subgroup variation to between subgroup variation, o Hs important in interpreting the
control charts to form subgroups with an understanding of the posible sources of vation affecting
the process results. Conider the following example: A production proces cont of four parle,
operations. Li sureste that variation in process output should be studied with control chart 2 a
decisions o be made on how collect the data for the cart, There area variety al possible sampling
‘schemes that could be considere, Part could e taken rom each stream to forma subgroup or parta
from only one stream could e included inthe same subgroup or subgroup could he formed y aking
parts from the combined stream of output without regardto thr source, Foe numerical example alone
provides an example of possible reals obained using these tres methods.

Methods to collect data tom the output of a mut

ream (spindle) production process,

Method 1: A sioyoup cones

Sass VB
SE EEE

Every hour 16 part sample let by taking the pats rom four consecutive eyes fom ch steam.
‘The following van example of the data

Cycle of the Machine

Samples a co»
Stream ı E mo
Stream 2 2 BB
Stream 3 9 5 2
Stream 4 1 Lo»

‘There are three sources of variation captured in the data, Cole to Cycle variation i captured by diferent
columns in the array, stream to stream variation is captured by the rows ofthe array, and hour-ochour
variation is eaptured by diferent samples of 16 parts

an

v3

úAppencix À - Comment on Subgrouping (Cont)

Onesubgronpingschame wuld eto plo e average and range escola ofeach array of dts. Using
{hs eubroupng sche rn to Seam variation woud be contained wabin each subgroup Hour 15
hour etation nd quee gee ration woul contribute to dierencsbtwee los, Anc pos
"blesubroupng home would bet plot average ad range ofeach ow of ech array oat, With
{hbjroupagseheme eyo to vrai woul be email win cach subgroup ind hort Rou and
‘trim do Sn von woud conte to ferences between groupe

Bubgroupingby colama Eee 1
» a/ cn? » à pk Das con,
s/t 3 12003 sI IDA sun man

R A
sz) 2 m us Summuuss Su bu us
18 18 20 183. 35315 17 717 1033 $316 16 2 16 004
132 S82 6 BMS 2 Sm de Momo à

120 135 128

Kuna us na 125 ns 109 108 120
ara)

x
nee T 6 RE Ge 6

a 8 CD +

a a @ABCDER
Sun 6 0 wos Si 8 1 7 6 78 à
S18 15 13 15 M0? Se 90 9 9381
Si M 0 NUS Sa M M 0 Me
Sum a ke MT 6 6 602
mM
y

Data from 20 consecutive hours are used to construct control charts with each subroping method.

Method

1: Subgrouping by columa (Cycle)

‘This subgrouping scheme yields 80 subgroups often = 4. The average rangeis7.85,and the upper contre
lit forthe range chart 1791 unite, Within subgroup variation appear tobe stable using this method

Range Chart for Data Subgrouped by Column (Cycle)

16 UCLA

is
6 A

ase

> ES 0

‘Appendix A - Comments on Subgrouping (Cont)

X-Bar Chart for Data Subgrouped by Column (Cycle)

Method 2: Subgrouping by Row

‘The second subgrouping scheme yields 80 subgroups ofsizen = 4 The grand average s 11.76units and the
average range 3284 units. The control its fr the X-Aar chart are 13.89 and 970 unit, andthe upper
‘control limit forthe ange charts 8 48 unit. Th control chart fortis subgrouping scheme are shown
bel.

Range Chart for Data Subgrouped by Row (Spindle)

Uola

ye

‘The control charts forthe diferent subgroupig schemes ae very diferent even thoug they ara derived
from the same dat. The X-bar char for data subgroup by row shows à patera: All the pont corr
Spondingtospindle are noticeably higher than thew rom the cther streams The first bar chert docs ot
‘reveal the stream dllerences because readings fom ach stream are averaged to obtain euch X Dar vale.
‘By grouping the data diferent, he charts adress deren questions. Forthe iat et of chart, steam to

108

Y 5 >

Aprendiz A - Comments on Subgrouping (Cont)

stream variation uted asa bass comparison The R har checks to see hat stream to steam variation
{is stable over time and the X-bar chart compares cycle to yee and hour to hour wth stream to steam
‘aration The second sto charts use ee to eee variation sa ass far comparison. The Rehart checks
Lo ett the eee to eel variation i stable over ime and the X-bar chart compares stream o stream
‘aration and hour to hour variation with the base level of variation established bythe range, cele to
‘ce variation, Since the stream to stream differences reso large contollimits inthe st set ofeharts
‘re much wider than the second set.

‘With the second suhgrouping mothod the data could be used to create four separate sets of control charts
rom the data, one for each stream,

RChars
Stream 1 ‘seam 2 Steam Streams

X-Bar Charts
Steam 1 Stream 2 Steams Steam 4

‘This comparison of the chart shows tha the average ofthe third stream ¡higher than he others ad the
Individual processes ae out of control The base level of variation used for study o the result rom each
Stream is le to ye varation os reflected in the rang. For each stream the efect of hour to hour vr

ation are shown onthe X-bar chars By plating the chats usa the same scale th eel and variation or
‘ich stream can bo compared

Method: ‘Thethin! method ofsampling would beta sample the part rom the combined output from all
four streams. This method gives some insight into the variation has sento the ext process Dut,wecanno
longer differentiate which trem produced the par. Provided the art inthe combined streum ae mixed,
(he anges reflect a mitre of steam to stream and cycle to cela variation, The X-bar vales conto,
lution, hou to hour variation. Ite hour to hour contribution to variation large enough, that contri
tion willbe seen as out of contra points on the X-bar chart

an

O En

‘Appendix A ~ Comments on Subgrouping (Cont)

Combined Output R Chart
16

“laa AA

Y ur

ony

Combined Output X-Bar Chart

er

‘Tho R chart checks to af stream t stream and cyl to cycle variation consisten over time. The X-bar
‘hart answers the question "Is the variation in X-bar values what would be expected Y ce to ele and
stream to stream variation were the ony kinds of variation prevent in the pros, o, there atonal
‘change hour to hour?”

‘Asa general ral, the variation that is represented within subgroups shouldbe the Kind of variation that is
lire tobe the leat significant orleast interesting a subject far current stud). nll ease, a method of

subgrouping shouldbe used that il allow questions about the effects af potential sources o aration ob
snowed

1850

> E

APPENDIX B
Overadjustment

Overadjustmentis the practice of treating each deviation from the tant sit were th result ofthe action.
‘ofa special caus of variation nthe procesa Ia stable process adjusted onthe basis of exch measurement
‘made, then the adjustment becomes an ational source of variation The allowing examples demonstrate
‘this concept. The fist graph shows the variation in results with no adjustment. The Second graph shows the
variation results when an adjustment is made to the proces oeatpensate fr each deviation from the
arret The third graph shows variation in results when adjustments are made Lo compensate only wea the
last result was more than one unit from the target. This hid sei an example of compensntion to tay
‘thin a set of specifications. Each method of adjustment inereases the variation in the output, since the
‘aration without adjustment i stable ee Appendix H, Reference 4, Chapter 1D.

esas wit uan

Normas

Ross we adjustment o compensa o a davon rom tral

Note torso
var

Tags wit RETO NT BATON NT
atan wes gear an +

APPENDIX C

Selection Procedure for the Use of the Control Charts
Described in This Manual

een

Noto: is char assumes ne mess
‘urement system has boon assesses
and appropriate

1m

Y EN >

ad
APPENDIX D

Relationship Between Cpm* and Other Indices With
(USL - 1) = (T- LSL)**

tt r us

Pe

1. 70
is 7 ust

12 CPL CPU ox com

oon 2 1 pb 15016 OT 1
ise T ust

SBC GNU ook Con

won 2 8 4» 6 zug
use r ust

e GG ou cok cam

won 2 3 sp
ust r us.
LL GC Cru co com
one vw
USL-LSL,
+ Gm = ESE here “T= specification tape, x given
Ban Ë is

individual sample reading and = total number of individual sample readings.

** LA. Chan, SW. Cheng and PA. Spiring, "A New Measure of Process Capability: Cyn Journal of
Quality Technology, Vol. 2, No July, 1980, p16. Reprinted from theslourna of Quilty Technol
95: A Publication the American Soc for Quality Contra.

a

Y EN <p

1e

APPENDIX E
Table Of Constants and Formulas for Control Charts

Fand Charest ands Charter
‘lat for Ghat for =
Aves ‘areas ats or
® Char or Range (R E Santa Devons 6)
Dior for Dion tor
Factor Esimateat — Foctorstor Fugorsfor Batimate st Factors for
Suberoup Cont!” “Standard Goo Can "Standard Conti)
Sue” mite Down, _ mie Um Dean Limo
» a 74 be m CE Bd
EC Cra = See ao om ~ 8367
FE 1e CC see 2 250
4 om 200 = tm ia toma = 2266
5 osm a = ama ooo > 2069
go ase = 204 1287 0955 on 1970
E
8 O5 AT a LE soso as 388
2 os 200 OGM 186 Ie Om 02 Lad
10 O8 So OU LT OS OST ase 1116
HO OMS om os 14 our oo oak 167
102 ds ams INT OMG aa 101
0% a OO 18 GO OI 08 108
M OMS OO 02 16 GMT a ooo 134
150% AZ OSA 163 OO Dada Lo
19 One ose os 167 om 09885 as 1552
1 O2 a E
JM RE
J9 OT a Da 047 10
MO LK Lam
Om ame oats 166 06 ose os
BOOT GS OO 1566 ra se
Bm OMS 167 OS Or ss
CS Beer ee SS
E Ma
Venetien Rs AR VCC AS
Vas DR
Lk DR
EPS

* From ASTM publication STP-15D Manual on the Presentation of Data and Control Chart Analysis,
1976; pp 194-196, Copyright AST, 1918 Race Street, Pain, Perte 19103. Reprinted
‘wth permission,

us

Y E >

[APPENDIX E - Table of Constans and Formulas or Control Chars (Cont

Medina Chart, ++

Chart or Indviuats®

Char for Chart for

Mediana divas
oo Char fr Ranges) © Chart fr Ranges (0

Disons for Divo for
Factors for Estimate of Factor Factosfar Estimate af actors for
Control Standard Control” "Control" Standard Control
mits Deviation ime me _Devition Lim
Subgroup =

EN & de DD E de Ds De
2 1880 108 = 260 11% = 3267
3 List 183 [os 1m 1m 2514
4 0396 2050 Dome uam 205 Ber}
5 0801 2305 EE en
6 0548 2534 = 20m Lt 2a 200
7 0508 2704 0076 19% 1m 276 0076 192
8 04 2 06 18 A RAAT 0196 1864
5 ou 2970 Où 186 100 2070 014 1316
1 ies 308 02 m 0 SO 0223 LT

verg.Leig= a ÁS

UclxLcly= FE ER

uch,
OLA

D
DR

+ From ASTM publication STP-15D, Manual on the Presentation of Data and Control Chart Anaya,
1976; pp 134-196, Copyright ASTM, 1916 Race Steet, Philadelphia, Pennsylvania 19103, Reprinted,

seth permission.

‘Factors Died from ASTM-STP-15D Data and Efcency Tables Contained in W.d. Dixon and

Ea. Massey Ir, Introduction to Statist! Anais, Third Edition, 196, Page 488; MeGraw Hl

Book Company, New York

ue

oe ts

APPENDIX E - Table of Constants and Formula for Control Chart (Cont)

Attribute Charts

chat for proportion af units nonconforming, rom samples not necessarily of constant size:

UCl,, Lely =p + TBH

D

ops spt

p chart for number of units conforming, fom samples of constant sie:

VL LOL ap a 3 (BCP

‘chart for numberof onconformites, from samples of constant size

ven Lou ers HE

‘chart for number of nonconformitis per uni, rom samples not necessarily af constant sie:

26m

of

Mero: Guido for selection of chart or attributes:

ve, Lely

Nonconfoming
nice Une Nonconfarmitie

(Simple, but seeds
constant sample see)

PROPORTION
(ore comple, but
adjusts to understandable

» “
proportion, and can cope
‘th varying Sample sizes)

DES

APPENDIX F
Standard Normal Distribution

Po = the proportion of process output beyond a particular value of interest (uch ea speifiation Limit)
‘lt is standard deviation units avy from the process average or a process ha sin statistical control
andis normally distributed). For example, fs = 2.17, P, = 0180 018% In any actual situation, this pro»
portion is only approximate

E

Ed
E
#
E
E
22
bl
24
E
Ej

=

Appendix G

Glossary of Terms and Symbols

‘These are intuitive descriptions of terms used inthis manual For operational and mathematical definitions

see References in Appendix

Terms Used in This Manual

‘Advanced Statistical
Methods

‘Attributes Data

Average (see also Mena)

Awareness

Statistionl Methods

Binomial Distribution

aus

nd-fteet Diagram

Central Line
Characteristic

‘Common Cause

More sophistiated techniques of statistical process analysis and
control than ncludedin Basi Statistical Methods; thiscanincide
‘moreadvanoed control chart techniques, regression analysis, design
Experiments, advanced problem-solving techniques, et

Qualitative data that canbe counted for ecordng and analysis. Bram-
ples include characteristics suchas the presenceof require label the
Installation ofall required fasteners, the absence of errors on an ex.
pense report. Other examples sro characteristics chat are inherently
measurable the, could be tread as variables data), but where the
‘esulsare recorded ina simple ys/n fashion, such as accepta of
A shaft diameter when checked on golso-go ge or the presence of
Any enginering changes on a draving Altibuis ata tre usually
tathered in th form af nonconforming units or of nonconforml.
ties; they are analyzed by p, np, cand control charts. (See also
‘Variables Data)

‘Thesum of values divided bythe number (sample siz) of values de:
‘ignated ba br ver the symbol forthe values beng averaged: X
(bars the average ofthe values within a subgroup; Y (X double

bar istheaverage of subgroupaverages; X X ide-hanitheaverage
of subgroup medians; R is th average of subproup ranges.

Personal understanding ofthe iterelatonship of quality and produc-
Livy, direting atenton to the requirement for management com.
mitment ond stats thinking achive never-endingimprove-

Apples the theory variation through use of basic problem-solv
ing techniques and statistical process control; includes control
Char onstrucion andinterpretalon or hoth variables and atrib-
‘utes data) and eapabllity a

Adiserete probably distribution for atteibutes data that apples
toconforming and nonconforming units and underlies the p and
mp chart

‘A simple too or individual or group problem-solving that uses a
rape description of the various process elements to analyze poten:
al sources of process variation Also called fishbone diagram after
lis appearance) or Ilka digram (after its developes).
Thelinoona control chart tha represent he average value ofthe
items eng lated.

A distinguishing feature of process ots output on which varie
bles or attributes data can be collected,

A source of variation that effects all the individual values ofthe
‘Process output bring studie in control chart analysis appears as
part of the random proces vaio.

1092

Y E © 2

Appendix - Glossary (Cont)
Consecutive

Continual Improvement
in Quality and Productivity

Control
Control Chart

Control Limit

cusum

Detection

Distribution

Individual
Location

Mean
Median

Units of output produced in successin; basis for selecting
samples,

‘The operational philosophy that makes best use ofthe talents within
the Company to producepreductsofnreasing quali fr our custom.
ers in an iereaingly ecient way that protec the return on inves
‘ment to our stockholders. This sa dynamic strategy designed to en.
hance the strength of the Company inthe face of present and future
market conditions. contrast with any state strategy that corte
fexpliciy or imply) some particular level of outgoing dect sin.
cable

See Statistical Control

group

A graphic representation of a charneteristie fa process, showing
plotted values of some statistic gathered frm tht characters, à
central line, and ane or two control limits. It minimizes Usenet
economic loss from Type Land Type I errors, has base uses:
Asa jument o determine fa process has ben operating in state
al control, and 0 aid in maintaining east contra

Aline (rline) on control chart used a hass or judging thesta-
bility ofa proces. Variation beyond a control limit i evidence that
special causes aro affecting the process. Control limits mre cales
lated from process data and aro not to bo confused with engineering
specifications

‘An advanced statistical method that uses the current and recent past
proces data to detect small o moderate shi nthe proces average
fr variability. CUSUM stands far" cumulative sum” o devitins rom
the argue and puts equal wright on the current and recent past dat
A pastoriente strategy that attempts 6 identify unaceptable ut-
Frater has been produced and then separate rom the good out
Put. (See also Prevention)

A way of describing the output of a sable system of variation,
‘which individual values are not predictabe but in which the
‘ames asa group form à pattes that can he decriod in terms of its
Jocation, spread, and shape. Location is commonly expressed by
themean or average, orhy the median;spreadisexpressedin terms
ofthe standard deviation o te range oa sample; shape involves
‘many characteristics such as symmetry and peakedness, but these are
‘often summarized by sing the name of common distribution suchas
‘the normal, binomial, or Poisson.

AA single uni, or a single measurement ofa characteristic often de-
‘ote by the symbol X

{A general concept forthe ypeal values central tendency a dist
‘ation

‘The average of values ina group of measurements

‘The middle valo in group of measurements, when arranged fromm
lowest to highest if the number of values even, y convention the
average othe mile two valuecisusodas he medien. Subgreupme-
‘hans form the basi fra simple control chart for process loca-
tom. Medians are designated by a tilde (7) over the symbol forthe

individual values: X is the median of «subgroup.

-100-

‘Appendix G - Glossary (Cont)
Moving Range

Nonconforming Units

Noneonformity

Normal Distribution.

Pareto Chart

Poisson Distribution

Prevention

Problem-Solving

CO E

‘The difference between the highest and lowest vale among two or
more successive samples such tata each additonal ata pot ls o
tained, tb rango associated wath that point compte Ey adding the
‘new point and deleting the “ode chronological point, 5 that each
rang calculation bas a lest one shared point from the previows ange
‘elation. Typically, the moving range is ulized on control charts
{or individuals and uses two-point consecutive points) moving anges
most ofthe time,

Units which do not conform 10 specification or other inspection
standar; sometimes called iscropant oF defective units. p and np
control charts are used to analyze systems producing nonconform
ing

Aspeciicoccurenceofacondiion which doesnot conform toa speci
fleation r other inspection standard: sometimes called a discrepancy
ora defe An individual nonconforming unit can have the poten:
tial for more than one nonconformity (e. a door could have several
‘ents and dings a unesonal check of ccarvuretor cold even oa
number of potential dserepanciee cand u control charts are sed
{analyze systems producing nonconformities

A continuous, symmetrical, bell-shaped frequency distribution for
variables data thats te si for the control charts for variable
"When measurements have e normal distribution, about 68267 fal
individuals be withinplasor minus one standard deviation unico?
le mean, about 95.44% le within plus and minus two standard devine
tion units of the mean while about 90:75 le within plas and minus
thre standard deviation units of the mean, These percentage are the
‘bass for control mis and control chart anal ice subgroup ave
eragestend tbe normaly distributed even the output as vie Le
ob. and fr many eapability decision sine Ih output of many in.
‘usta processes follows the normal distribution),

‘A means ofelearly communicating quality expectations and perorm-
noe it consists of I) a criterion tobe apple to an objector to à
group, (2) atest he objeto ofthe group, ($) decision yesor no»
the object or the group dd or did ot meet the enterion

A siple tol fr problem solving that involves ranking ll potenti
problem areas or soures of variation according to their contribution
{cost orto total variation. Typically afew causes account for mast of
the cost (or variation), a problem-solving efforts are best prone
{o concentrate an the “vial few” cases, temporary ignoring the
Seiad many

Adisret probability distribution or ateributes data ta
to noncontarmities and underlies the and u control charts

Afuturo-orented strategy that improves quality and productivity by
Airecting analysis and ation toward coreting the process ise
Prevention ls consistent vih a philosophy af never-ending Im-
provement. (Se ako Detection)

applies

‘The process of moving from symptoms to causes (special or com.
mom) to actions that improve performance. Among the basic tech.
niques that can De use are Pareto chars, causo-and-efectdagrams
and statist process contre techniques

ie

Y E ep

Appondbc & - Glossary (Cont)
Process

Process Average

Process Capability

= Variables Data Case
- Attributes Data Case

Process Control

Process Performance

Process Spread

Quadratic

Randomness

Run

‘The combination of people, equipment, material. methods, and env
ronment that produce output = à given product ar service, A process
fan involve any aspect our business. A Ke tcl fr managing proc
Ser I statistical process control.

‘The location ofthe distribution of measured values fa particular
process characteristic, usally designated as an overall average,

8.

‘Tho total rang ofa stable process inherent variation (6)

DA process's inherent capability is defined as ne,

2) À process capability of meeting specification. # output within
specification) can ho estimated by indices that consider process center
Ing as wel as spread (eg, Cy, with some assumptions. However,
more preciso methods also exit fr this estimation,

A process's capability ls usualy defined asthe average proportion oF
‘alco defector defectives, From control chart, for example capi

ltyis defined as P , €,0r where capability refers iretyL he aver:
ae propartion orrut ofutput hat dons not meet specification (ras

ALP, te, the percentage output within speeißiention).
Soo Statistical Process Control

‘The total range ofa proces otal variation (64),

‘The extent to which the disteibution of individual values ofthe
process eharactaristle vary often shown asthe process average
lus or minus some number of standard deviations. (eg.
“a 307,

For pertaning to a second order mathematical relationship od
‘common example of something thats quadratic sa parabola.

AA condition in which individual values are nt predict
‘hey may come frm à fiable distribution.

though

"The proces of selecting units fora sample fis, in such a manner
that all combinations of units under consideration have an qual
chance of being selected as the sample

‘Thediferenceetween the highest and lowest values ina subgroup, a
sample, oF à population

Asubgroupguthered in such a manner 4 to give the maximum chance
forthe measurements in each subgroup to be alike andthe maximum
‘hance fr the subgroup o differ one from he other This subgroup
ing scheme assumes devine to determino whether or nat a proces à
ation appears 1 come frm constant system of chance eases,

A consecutive number of points consistently increasing or decreasing,

boraboveorbalow the central line, Can be evidence othe existence of
Special causes of variation

case

Appendix - Glossary (Cont)
Run Chart

Specification

Spread
Stability

Stable Process
Standard Deviation

Statistie

Statistical Control

Statistical Process Control

Subgroup

A simple graphic representation of a characteristic of a process,
‘showing potted values of some statisti gathered from the process
(often individual values) and a central line (fon the median af
the values), which can be analyzed for rans. (See also Control
Chart)

In process controlapplications,a synonym with Subgeoups thi use
istotll diferent rom the purposeafprovidingan estat ofalarger
Aroup of people, tems, te

‘general concept for the overall patter forme hy a distribution of
values

‘The Greek letter used to designate a standard deviation,
‘A source of variation that isintermittnt often unpredictable unsta-
‘be; sometimes called an assignable cause. ee ira ty a point be.
yond the control limits ora run or other non random patera of
Points within he contra mit,

‘The engineering requirement or judging acceptability of particular
charneteristie. A specications never tobe confused witha control
limit Kal, a specication tis directly oor e compatible wth the
customer's Gaternal and/or externa) requirements or expectations
‘The span of value from smalls to largest ina distribution. (Se also
Process Spread)

‘The absence of special eauses of variation; the property ofbeingin
statistical control

A proces that sin statistical contro

A measure ofthe spread ofthe process output or the spread ofa sam-
ing statistic from the procs (eg. of subgroup averages) de.
noted by the Grea letter 6 (sigma) ar the letters. Por sampl sea
dara deviation)

A salue calculated from or based upon sample data ng, subgroup
‘average or range) sed to make inferences about the process that
Produced the output from which the sample came.

‘The condition descibinga process from which all special causes of
variation have been eliminated and only common causes remain,
Le. observed Variation can De attributed Lo a constant system oF
chance eases evidence on a control char by the absence of points
bond the control limits snd by the absenoe of non-random pet
terns or trends within the control ints,

‘The use of statistical technique such s co
Process oritsoutputs soasto take appropriate actions to achieve and
maintain a state of statistical control and to improve the process
capability

One ormore events or measurements used to analyze the performance
ofa process, Rational subgroup are sully chosen so that the vari
ation represented within each subgroup ss small a fest forthe
roces representing the variation from common causes), and so
that any changes in the process performance tre, special causes)
wi appear as diserenes betwen subgroups, Rational subgroups are
‘apically made wp ol consecutivo pieces although random samples
are sometimes wre,

charts to analyzes

180

Y E ep

Appendix G - Glossary (Cont)
‘Type L Error.

‘Type I Error.

Variables Data

Variation

Inherent Variation
Total Variation

Zone Analysis

Rejecting anassumption thats rue takingactionappropriatfor
‘a special enue when in ac the process has not changed: overeot
tol

Fling to reject an assumption that i fale: e, nt taking appropri
aleacion when in ht the process isaected hy special enuneszun.
encontra:

Quantitative data, where measurements ae used for analysis Bram-
pies include the diameter o bearing journal in milimeter, the os.
Ing effort ofa dor in newtons the concentration of electrolyte in per.
cantor thetorqueofa fastener innewton-meters,X and, X ands,
‘median and individuals and moving range control charts are
‘ied for variables data (See alto Atributos Data)

‘Theinevtabe difference among individual outputs ofa process; the
sources of variation canbe grouped into two major lasses: Common
‘Causes and Special Causes,

‘That process variation due to common causes only, estimated by

‘That process variation due to bath commen and special cause, esti
mated by dr

‘Thisisa method of detailed analysis ofa Shewhart contra chart which
divides the X-bar char between the control mit nto three equi
tant zones above the mean and three eqidstant zones below the
‘ta, These zones are sometimes refered s “sigma” zones (gra
here isthe standard deviation of the AVERAGE distributiva, not the
Individuals). ach one is assigned a probability forthe proportion ot
points expected tbe found there, provided the data normaly de
buted (ie, vn control). Por example, the zones adjacent to the
‘ean are assigned prbeblities of 341, the newt zones have apr
bly of 196and the outer zones have a probability of 02135 Thear-
‘as beyond the upper and lower contrallimitareeah assigned prob.
bof 0015, Data may then be ested for natural pateras based
On where the data pont i in relation to hese zones. Probables or
Range charts are dependent on Sample size, whi probabilities for at
tribute charts are based on binomial or poison distributions. The
rules o thumb derived from this system may be used asa early are
ing system fr subtle proces changes which may not be reflected as
points bayonlthe contra ini. The readers referred othe Western
Biere “Statistical Quality Control Handbook” pp.25-81, 180-188
{or mor information, (Appendix I, Reference 7)

is

‘Appendix - Glossary (Cont)

Symbols ns Used in This Manual
e A multiple of Fused to calaltetho control limits for averages; tabled in Appendix E
LA A multiplier of Fused to calculate he control mis or medians; tabled in Appendix,
» A multiplier of used ta calculate the control limits fr averages; tabled in Appendix
Buße Multipliers o used to alle the lower and upper control ints, respectively, or
sample standard deviations: tabled in Appendix E
. ‘The number of nonconformiiesin a sample; thee char is described in Chapter M,So-
con
© ‘The average number of noconformitis in samples of constant size
“ “The diisr of usd o estimate the process standard deviation; abled in Appendix.
o ‘The capabity inde for a stable process, ypially defined as (USE LSL)
Ca ‘The capability index fr a stable process, typically defined as the minimum of CPU oF
ome
om ‘The lower capability index pically defined as LU)
E77
ou ‘Toe upper pity inde, il died as EL)
ns,
oR ‘The capability ratio fora stable process, typical defined as
a vey Wii
e A divisor of usd o estimate the process standard deviation; tabled in Appendix E
Da Da Muliplirs of Fused to caleulate the lower and upper conto] limits, respectively, or
rangés table in Appendix.
Fe A multiplier of used to calculate contol ints for individuals tabled in Appendix E.
x ‘The number of subgroups being used to caculate contol mts
Lot ‘The lower control init LCLx. LEL4. LCL, te, are, respectively, the lowor control
limits for averages, ranges, proportion nonconforming, et
ist ‘The lower oginerng specication lint
MR ‘The moving range of serios of datapoints used primarily on chart fr Individual

‘The numberof individuals in subgroup; the subgroup sample size
‘The average subgroup sample sie.

as

Y E ep

‘Appendix G - Glossary (Cont)

m

"e
»

F

Py

PR

nom

uch

ust

‘The numberof nonconforming items in a sample of seen; the np char is described in
Chapter I, Setion 2.

‘The average number of nonconforming items in samples of constant sien.

‘The proportion of units nonconformingina sample; the p-chart is diseased in Chapter
ML, Section 1

‘The average proportion of uit nonconforming in series of samples,

1 performance index, ypcaly defined us (USL=LSL)
‘The pert ‘ply dened as SL

6%
‘The performance rato typically defined as _ SE
to Wr

‘The performance index, ypicaly defined asthe minimum of USL-R op Roush,

‘The proportion of output beyond a point of interest, such as particular specication
limit, standard deviation unta away from the process average.

‘The subgroup ange highest minus lowes value; th R chart discussed in Chapter I.
‘The average rang of seis of subgroups of constant size

“The average of serie of average ranges of subgroups of constant sz.

“The median rango ofa eres of anges from subgroups of constant size

To sample standard deviation for subgroups; hes cart is discussed in Chapter, Sec-
don?
‘The sample standard deviation for process

4 is dieussed in Chapter I, Section 5,

‘The average sample standard evito ofa sers ofsabrous, eghedifncessany by
sample ie.

A unilateral engineering specication mi.

"The numberof nonconformiis per unit in a sample which may contain more than one
nische u chart diseused in Chapter I, Section &

"The average numberof noneonformities per uni in samples nat necessarily o the same

‘The upper control mit: LCL, UCL, UCL ee, are respective) the upper contro
limits for averages, ranges, proportion nonconforming. ee

"The upper engasering speciation limit

An individu valu, upon wich other subgroup statistics are based the chart for indi
‘ial is discuss in Chapter I, Section

“The average of values in subgroup; the X-chat i discussed in Chapter I, Section 1.

-10-

> En Y

‘Appendix G - Glossary (Cont)

x

x

sigma)

Oxo. te

‘The average af subgroup averages (weighted if necessary by sample ic; he measured
proces average. Not: In his manual, is used or the process averageof an individuals
thar (Chapter I, Section 4) eventhough i represents only one level of averaging (he
individual data pont), 1 avoid confusion with X which otherwise aba refers to sub-
ros average

‘The median of values in a subgroupthe chat for medians discussed in Chapter I, See
ion 3 tide

‘The average of subgroup medias; the estimated process median, O tilde ba

‘The numberof standard deviation unit rom the process average to a value of intrest,
suchas an engineering specication. When used in capability ascessment, Zen th di

tance tothe upper specification limit, Zus she distanceto the lower pedfeation limit,
and Zi the distance tothe nearest specification limit

‘The standard deviation ofthe distribution individual values ofa proces characteristic

‘An estimate of the standard deviation of proces characteristic

‘The standard deviation ofa statistic based on sample process output, such as the stan:

‚dad deviation ofthe distribution of subgroup averages wich so //5), the standard
<eviation ofthe distribution of subgroup ranges, the standard devietin o the distrib
tion of proportion af nonconforming tema, ee,

‘The estimate ofthe standard deviation ofa proces using the sample standard deviation
ofa St of individu about the average of the st.

‘The estimate ofthe standard deviation ofa stable process using the average range of sub-
grouped samples taken from the process, usualy within the context of contol chats,
‘ete the d actor i tabled in Appendix E

Y E >

OE

APPENDIX H
References and Suggested Readings
1. Walter A.Showhart,Beonomic Control of Quality af Manufactured Produc, Va Nostrand, 199;
republished ASQC, 190, Available rom the American Socie for Quality Control, 611 Bast Wis
consin Ave, Miva, WI 53202,

2 Walter A. Shewhart, Statistical Method fram the Viewpoint of Quality Control, Ete by W. Ed
‘wards Deming, the Graduate Schoo, Department of Agriculture, 199.

3. W. Bavard Doming, Quay, Productivity and Competitive Position, Massachusetts Insitute of
‘Technology, Center for Advanced Engineering Study, 1982

‘Out ofthe Crisis” Massachusetts Institute of Technology, Cente for Ad
‘vanced Engineering Study, 198%

5. American National Standards Institute, Guide for Quality Control and Control Chart Method of
“Analyaing Data (ASQC Standards BI-1958 and B2- 109Q/ANSI 211-1958 and 212-1968, w

‘American National Standards Institute, Control Chart Method of Controlling Quality During
Production (ASQC Standard BS-1958/ANSI 13-1058, revised 1970).

NOTE: __‘Theabovetwo booklets ar available from the American Society for Quality Control,
611 East Wisconsin Ave, Milwaukee, WI 85202.

5. American Society for Testing and Materials, Manual on Presentation of Data and Control Chart
‘Analysis (STP-16D), 1976 Available from the ASTM, 1916 Race Str, Philadelphia, PA 1910,

7. Wester Electric Co, In, Statistica! Quality Control Handbook, 1056. Available fram : LD.C,
Commercial Sales, Western Electric Company, P.O. Box 20205, Indianapolis, Indiana 46226.

8. Harvey C.Charbonneauand Gordon L Webster, Industrial Quality Control, Prentice-Hall Ine,
1978,

9. AchesonJ. Duncan, Quality Control and Industrial Staite, Richard D, Irwin Tne, Fourth Ed
tion, 1978

10. Eugene L Grant and Richard 8, Leavenworth, Statistica! Quality Control, MeGraw-Hl, nc,
Fit ion 1980,

11. Kaoru Ishikawa, Guide Quality Control, Asan Productivity Organization, Revised Edition,
1916

12. JM Joran Frank M Gryna, Jr, and R. Bingham, e, Quality Control Handbook, McGraw
Hi, ne, Fourth Edition, 1990,

18 lls R Où, Process Quality Control, McGraw-Hill Ine, 1975

14. Bert Gunter, “Use and Abus of €

parts, Quality Progres, January 1969, March 1989, May,
1969 and July 1980.

15. ASQC Automotive Division /AIAG, Measurement Syuems Analysis Reference Manual, AIAG,
100.

16. L.J.Chan, SW.Cheng.and A Spring, “A New Measureof Process Capability: Cyq,"Journalof
Quality Technology, Vel. 20. No 3,198, yp 162-176

-159-

€ E ee

Appendix H - References (Cont)

n.

18

2.

a.

General Motors Corporation, Key Characteristis Designation System, GM-1805 QN

Fred A. Spisng “Assessing Process Capability inthe Presence of Systematic Assignable Cause”
“Journal of Quality Technology, Vol. 28, No.2, Apri 1801

‚John T. Herman, “Capability Index-Buough for Process Industries?” Proceedings, ASQ 43e
AQO, 1989.

Robert A. Dovich, "Statistical Terorists” Quali in Manufacturing Mogasine, March-April,
002

BAF. Bisel, "How Reliable Is Your Capability Index”, Applied Statistics, Vol 39, 1900, pp
831-800,

R.A. Bayles, “The Tague Capabliy Index” Journal of Quality Technology” Vl. 28,1991, pp.
136

2. Wiliam W. Scherkenbuch, Deming’ Road o Continual Improvement, SPC Pres, In, 191.

Donald J. Wheeler, David 8. Chambers, Understanding Statatical Process Contra, Statistical
Process Controls, Inc, 1986

we.

Douglas C. Montogomery Introduction o Statistica Quality Control, ASQC Quality Pres, Se
ond Eden, 101

Leonard A. Doty, Statistical Process Control, ASQC Quality Pres, 1981,

1 Peter D. Mauch, Basic SPC: A Guide For the Servico Industries, ASQC Quality Press, 1991.

Bert Keats and Douglas C. Montgomery, Sato! Process Control in Manufacturing, ASQC
Quality Press, 1991

Gary Falles, PhD, SPC for Prosttiners Special Cases and Continuous Processes, ASQC Qual
Sty Pres, 10,

ASOC Statistics Divison, Static! “How-To Techniques Series, ASQC Quality Pres (15 Ve
As), 1970-101.

Victor, Kane, Defect Prvention-Useof Simple Statistical Tool, Marel Dekker, ne and ASQC
ality Press 1080.

ASQC, Definitions, Symbols, Formula, ond Tables far Control Charts, ANSUASQC A1-1981.

-100-

O ae

APPENDIX!
Reproducible Copies of Control Chart Forms

1612

‘Supplier/SPC Manual User Fandback Process

Consistent with the concept of continual improvement, hie automativ Industry statistical process contr!
(SPC) manual is being subjected toa formal anual review/nevision process dura he month ef October ot
«ach calendar year talinewith the concept ofeastomer satisfaction, tis anal review vil email considera.
ion o not only any applicable vehicle manufacturer requirement changes fot yer to ar but sso af
foeiback from users af the manual forthe purpose of making it more value-added and effective to the
‘automotive industry and user communities, Accordingly please fel ree to offer in wen, your feedback
comments, bath pro ad con, relative tothe manual’ understandably, "user Miedlinee ee in the

‘aren indicated below. Please indicat speite manual page numbers, where appropriate, Forward yore
facie tothe adres indicated below:

Your Name

Representing

‘Spi arpa Name
Actress

Pe
Please list your lp oo automotive customers and har locations

ana Ta =
one D
Gas an
Feedback Comments
"srach aceon
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benscommnt%e: ges nora te cpa
oe
=

20200
Soma, Mich 49034

SIRSANOS EL RE RERO ar

LWVHO JOULNOO HL AS OSIVNOIS NAHM NOUDY AALIBLUOO DIV OL NOA ¿TH TIM SALON 33H 0310N aa
NOS SALSA INANUNSVaN LO SANOVN SCO INSVINORUNG S TIESLVA 31403 ZONVHO ANY

13345 9018530044

En

‘THVHO TOHLNOD

CONTROL CHART

[AVERAGES (x DAR CHART) action,

= ACTION INSTRUCTIONS

Teen De een = RANGES (CHART)

ATTRIBUTE CONTROL CHART FORMULAS

aus seen
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CONTROL CHART FOR ATTRIBUTE DATA

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[aN GNANGE I PEOPLE, EQUIPMENT, MATERALS, HETHOOS. ENVIRONMENT ON MEASUREMENT SYSTENS. SHOULD GE
ated these NOTES AL RE YOUTO TA COAREENE OR PROCESS PROVEMENT ACTION WHEN SOME BTM

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