STATISTICAL PROCESS CONTROL PRESENTATION
HarneetSingh379346
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Jul 24, 2024
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About This Presentation
STATISTICAL PROCESS CONTROL AND PROCESS CAPABILITY
Slide Content
Statistical Process
Control & Process
Capability
06-07.02.2021
Presented by:
Rajendra Tandon
Control & Process
Capability
06-07.02.2021
Presented by:
Rajendra Tandon
2
Drivers Of Quality
Product
Quality
Effective
Process
Control
Correct
Measurement
Drivers Of Quality
Product
Quality
Effective
Process
Control
Correct
Measurement
3
Statistical Process Control
&
Process Capability
Statistical Process Control
&
Process Capability
4
Agenda
✓Product control and Process Control
✓Voice of Process & SPC
✓Variation & its nature
✓Normal Distribution
✓Control Charts Concept –Variables & Attribute
✓Control Charts-Variable
✓Process Capability & Performance
✓Control Charts -Attributes
Agenda
✓Product control and Process Control
✓Voice of Process & SPC
✓Variation & its nature
✓Normal Distribution
✓Control Charts Concept –Variables & Attribute
✓Control Charts-Variable
✓Process Capability & Performance
✓Control Charts -Attributes
5
PRODUCT
or
SERVICE
THE
PROCESS
Inspect
Detect
Reject
Correct
Traditional Process Control(Product Control)
•Focus on Defect Detection
•Little or No reference to the process
•Goal Post Mentality
PRODUCT
or
SERVICE
THE
PROCESS
Inspect
Detect
Reject
Correct
Traditional Process Control(Product Control)
•Focus on Defect Detection
•Little or No reference to the process
•Goal Post Mentality
6
PRODUCT
or
SERVICE
THE
PROCESS
M ethod
E nvironment
P eople
E quipment
M aterial
Collect
Record
Analyze
Act
Listen Voice of the
Process
VOICE OF THE PROCESS
Process Control-Better Approach
PRODUCT
or
SERVICE
THE
PROCESS
M ethod
E nvironment
P eople
E quipment
M aterial
Collect
Record
Analyze
Act
Listen Voice of the
Process
VOICE OF THE PROCESS
Process Control-Better Approach
9.1.1.1 Monitoring and measurement of manufacturing processes
The organization shall perform process studies on all new manufacturing (including assembly or
sequencing) processes to verify process capability and to provide additional input for process control,
including those for special characteristics.
9.1.1.2 Identification of statistical tools
The organization shall determine the appropriate use of statistical tools. The organization shall verify that
appropriate statistical tools are included as part of the advanced product quality planning (or equivalent)
process and included in the DFMEA / PFMEA) and control plan.
9.1.1.3 Application of statistical concepts
Statistical concepts, such as variation, control (stability), process capability, and the consequences of
over-adjustment, shall be understood and used by employees involved in the collection, analysis, and
management of statistical data.
7
Requirement of IATF 16949
The organization shall perform process studies on all new manufacturing (including assembly or
sequencing) processes to verify process capability and to provide additional input for process control,
including those for special characteristics.
9.1.1.2 Identification of statistical tools
The organization shall determine the appropriate use of statistical tools. The organization shall verify that
appropriate statistical tools are included as part of the advanced product quality planning (or equivalent)
process and included in the DFMEA / PFMEA) and control plan.
9.1.1.3 Application of statistical concepts
Statistical concepts, such as variation, control (stability), process capability, and the consequences of
over-adjustment, shall be understood and used by employees involved in the collection, analysis, and
management of statistical data.
7
Requirement of IATF 16949
Processis the key factor that needs to be controlled for the success
of any organization
Voice of the Process
Through
SPC
of any organization
Voice of the Process
Through
SPC
➢SPCis one of the feed back system which control the process and helps
in prevention of defects.
➢Process Control System can be described as Feed Back system
➢This is a control system which uses statistical techniques for knowing, all
the time, changes in the process
➢It is an effective method in preventing defects and helps continuous
quality improvement.
Statistical Process Control
9
in prevention of defects.
➢Process Control System can be described as Feed Back system
➢This is a control system which uses statistical techniques for knowing, all
the time, changes in the process
➢It is an effective method in preventing defects and helps continuous
quality improvement.
Statistical Process Control
9
Quality and VariabilityyVariabilit
1
Quality
10
1
Quality
10
Everything is Different
•No two things are exactly alike….
•No two people are same…
Variability
11
VARIATION
The basic principle of SPC
•No two things are exactly alike….
•No two people are same…
Variability
11
VARIATION
The basic principle of SPC
Monitoring, Measurement, Evaluation and Control
?
Variation is inherent!
Variability
?
Variation is inherent!
Variability
Manufacturing Process
➢The products we produce are not exactly alike because of
many sources of variability.
➢Difference may be large or may be small but they are
always present
Variability
13
➢The products we produce are not exactly alike because of
many sources of variability.
➢Difference may be large or may be small but they are
always present
Variability
13
Sources of Variation
•Variability can come about due to changes in:
➢Material quality
➢Machine settings or conditions
➢Manpower standards
➢Methods of processing
➢Measurement
➢Environment
14
•Variability can come about due to changes in:
➢Material quality
➢Machine settings or conditions
➢Manpower standards
➢Methods of processing
➢Measurement
➢Environment
14
Two types of variation
1. Common causes of variation
2. Special causes of variation
Variation
15
1. Common causes of variation
2. Special causes of variation
Variation
15
Common cause of variation
Natural process variation
➢Built into the system
➢Consistently acting on the process
➢Unavoidable
➢Inherent in the process and common to all individual readings in time
periods
16
Natural process variation
➢Built into the system
➢Consistently acting on the process
➢Unavoidable
➢Inherent in the process and common to all individual readings in time
periods
16
A process operating under common cause is called under
statistical control. If only common causes of variation are
present and do not change, the output of a process is
predictable.
17
Common cause of variation
statistical control. If only common causes of variation are
present and do not change, the output of a process is
predictable.
17
Common cause of variation
➢Sudden in nature
➢Occur on an irregular basis
➢That affect only some of the process output
➢They are not common to all time periods
➢can cause process fluctuations which are large in magnitude
➢usually attract the attention of local people associated with the process.
18
Special Cause of Variation
➢Occur on an irregular basis
➢That affect only some of the process output
➢They are not common to all time periods
➢can cause process fluctuations which are large in magnitude
➢usually attract the attention of local people associated with the process.
18
Special Cause of Variation
19
If special cause of variation are present. The output of the process is
not stable over time & is not predictable.It is said to be out of
control
Special Cause of Variation
If special cause of variation are present. The output of the process is
not stable over time & is not predictable.It is said to be out of
control
Special Cause of Variation
20
Prediction
Prediction
If only common cause of variation are present and do not change, The voice of
the process is stable & predictable and is said to be under statistical control
If special cause of variation are present. The voice of the process is not stable
& predictable and is said to be out of control
Common and Special Causes
Prediction
Prediction
If only common cause of variation are present and do not change, The voice of
the process is stable & predictable and is said to be under statistical control
If special cause of variation are present. The voice of the process is not stable
& predictable and is said to be out of control
Common and Special Causes
Inherent variation
+
Special Cause of variation
Overall Process variation
Overall Process Variation
21
+
Special Cause of variation
Overall Process variation
Overall Process Variation
21
22
Variations & Types of Actions
Variations & Types of Actions
Actions on the System:
➢System actions are usually required to reduce the variation due to
common causes
➢Almost always require management action for correction
➢No amount of adjustment by production personnel will remove it.
➢Are needed to correct typically about 85% of process problems
23
Inherent / Common Causes of Variations
➢System actions are usually required to reduce the variation due to
common causes
➢Almost always require management action for correction
➢No amount of adjustment by production personnel will remove it.
➢Are needed to correct typically about 85% of process problems
23
Inherent / Common Causes of Variations
Local Actions:
➢Local actions are usually required to eliminate special causes of
variation
➢Can usually be taken by the people who are close to the process
(operator or other production services)
➢Can correct typically about 15% of process problems
24
Special Causes of Variations
➢Local actions are usually required to eliminate special causes of
variation
➢Can usually be taken by the people who are close to the process
(operator or other production services)
➢Can correct typically about 15% of process problems
24
Special Causes of Variations
Variation in Processes
Common Causes
•Variation inherent in a
process
•Cannot be controlled /
eliminated
•Can be eliminated only
through improvements in
the system
•Examples: -weather,
capability of a machine,
etc.
Special Causes
•Variation due to
identifiable factors
•Preventable
•Can be modified through
operator or production
services
•Examples: -tool wear,
preventive maintenance,
etc.
Common and Special Causes
Common Causes
•Variation inherent in a
process
•Cannot be controlled /
eliminated
•Can be eliminated only
through improvements in
the system
•Examples: -weather,
capability of a machine,
etc.
Special Causes
•Variation due to
identifiable factors
•Preventable
•Can be modified through
operator or production
services
•Examples: -tool wear,
preventive maintenance,
etc.
Common and Special Causes
Its important to distinguish between inherent and Special cause of
variation and treat them separately
Here ‘SPC’ plays a major role
26
Statistical Process Control
variation and treat them separately
Here ‘SPC’ plays a major role
26
Statistical Process Control
Estimation of process behavior:
Distribution can be characterized by :
➢Location
➢Spread
➢Shape
Process
Shape
Location
Spread
27
Distribution can be characterized by :
➢Location
➢Spread
➢Shape
Process
Shape
Location
Spread
27
28
Location
Spread
Shape
Or any combination of these….
Distribution
Location
Spread
Shape
Or any combination of these….
Distribution
Location
Mean or Average of a set of values
Process Behaviour
29
Spread
Range or Standard Deviation
Shape
Histogram
Mean or Average of a set of values
Process Behaviour
29
Spread
Range or Standard Deviation
Shape
Histogram
The Mean of ‘n’ numbers is the total of the numbers divided by ’n’n
.....xxxx
x
n321++
=
In Standard Mathematical Notation it is
−
−
=
ni
i
n
x
i
x
1
Mean
30
.....xxxx
x
n321++
=
In Standard Mathematical Notation it is
−
−
=
ni
i
n
x
i
x
1
Mean
30
Range
The difference between the largest and the smallest of a
set of numbers. It is designated by a capital “R”LowHi
MinMax
XXR
XXR
−=
−=
31
The difference between the largest and the smallest of a
set of numbers. It is designated by a capital “R”LowHi
MinMax
XXR
XXR
−=
−=
31
Standard Deviation
The average distance between the individual numbers and the mean. It is
designated by “s”
1
)....()()(
22
2
2
1
−
−−+−
=
n
xxxxxx
n
s
32
The average distance between the individual numbers and the mean. It is
designated by “s”
1
)....()()(
22
2
2
1
−
−−+−
=
n
xxxxxx
n
s
32
Histograms give a graphical view of the distribution of the values
It reveals the amount of variation that any process has within it.
Histogram
HEIGHT(Inches)
FREQUENCY
69 71
1
3
2
4
5
6564 66 6867 70 72
33
It reveals the amount of variation that any process has within it.
Histogram
HEIGHT(Inches)
FREQUENCY
69 71
1
3
2
4
5
6564 66 6867 70 72
33
By collecting sample data from the process and computing
their
•Mean
•Standard deviation and
•Shape
Prediction can be made about the process
Prediction about Process
34
their
•Mean
•Standard deviation and
•Shape
Prediction can be made about the process
Prediction about Process
34
Concepts and Principles of Control
Charts
35
Charts
35
Reasons for Popularity of Control Charts
1.Control charts are a proven technique for improving productivity.
2.Control charts are effective in defect prevention.
3.Control charts prevent unnecessary process adjustment.
4.Control charts provide diagnostic information.
5.Control charts provide information about process capability.
Control Chart
1.Control charts are a proven technique for improving productivity.
2.Control charts are effective in defect prevention.
3.Control charts prevent unnecessary process adjustment.
4.Control charts provide diagnostic information.
5.Control charts provide information about process capability.
Control Chart
Objectives of Control Charts
Primary Purpose :
To detect assignable causes of variation that cause significant
process shift, so that:
37
➢To reduce variability in a process.
➢To help estimate the parameters of a process and establish its
process capability
Primary Purpose :
To detect assignable causes of variation that cause significant
process shift, so that:
37
➢To reduce variability in a process.
➢To help estimate the parameters of a process and establish its
process capability
Lower Control Limit
Upper Control Limit
Center Line
Sample Number or Time
Sample Quality Characteristic
General Form of Control Charts
38
Center Line represents
mean operating level of
process
UCL & LCL are vital
guidelines for deciding
when action should be
taken in a process
Upper Control Limit
Center Line
Sample Number or Time
Sample Quality Characteristic
General Form of Control Charts
38
Center Line represents
mean operating level of
process
UCL & LCL are vital
guidelines for deciding
when action should be
taken in a process
A point outside of UCL or LCL is evidence that process is out of control:
Lower Control Limit
Upper Control Limit
Center Line
Sample Number or Time
Sample Quality Characteristic
Control Chart
Out-of-control signal:
Investigate assignable
cause(s).
39
Lower Control Limit
Upper Control Limit
Center Line
Sample Number or Time
Sample Quality Characteristic
Control Chart
Out-of-control signal:
Investigate assignable
cause(s).
39
Process Control
➢Means that common causes are the only source of variation present.
➢Refers to “voice of the process”, i.e. we only need data from the process
to determine if a process is in control.
➢Just because a process is in control does not necessarily meanit is a
capable process.
40
➢Means that common causes are the only source of variation present.
➢Refers to “voice of the process”, i.e. we only need data from the process
to determine if a process is in control.
➢Just because a process is in control does not necessarily meanit is a
capable process.
40
Process Capability
41
•The “goodness” of a process is measured by its process capability.
•This is a measure of the ability of the process to meet the specified
tolerances
•Compares “voice of the process” with “voice of the customer”, which is
given in terms of customer specs. or requirements.
41
•The “goodness” of a process is measured by its process capability.
•This is a measure of the ability of the process to meet the specified
tolerances
•Compares “voice of the process” with “voice of the customer”, which is
given in terms of customer specs. or requirements.
Control Limit vs Specification Limit
42
Specification Limits(USL , LSL)
•determined by design considerations
•represent the tolerable limits of individual values of a product
•usually external to variability of the process
Control Limits(UCL , LCL) base on data
•derived based on variability of the process
•usually apply to sample statistics such as subgroup average or range, rather
than individual values
42
Specification Limits(USL , LSL)
•determined by design considerations
•represent the tolerable limits of individual values of a product
•usually external to variability of the process
Control Limits(UCL , LCL) base on data
•derived based on variability of the process
•usually apply to sample statistics such as subgroup average or range, rather
than individual values
Variables Attributes
Control Charts
the characteristic is measured
on a continuous scale and
expressed as definite, precise
values
the characteristic is evaluated
on a go/no go,
acceptable/unacceptable basis.
e.g.
the diameter of a shaft,
% of carbon in a grade of steel,
weight of a part, etc.
e.g.
checking with a go/no-go gage,
checking for visual flaws,
tracking the number of errors made
in data-entry, etc.
Types of Control Charts
Control Charts
the characteristic is measured
on a continuous scale and
expressed as definite, precise
values
the characteristic is evaluated
on a go/no go,
acceptable/unacceptable basis.
e.g.
the diameter of a shaft,
% of carbon in a grade of steel,
weight of a part, etc.
e.g.
checking with a go/no-go gage,
checking for visual flaws,
tracking the number of errors made
in data-entry, etc.
Types of Control Charts
Identify if the product feature is evaluated according
to variables data or attributes data.
1. _____ A slot that has a measured depth of 1.513 in.
2. _____ The smoothness of a milled surface that’s
evaluated as acceptable or unacceptable.
3. _____ The diameter of a hole that’s measured with
plug gages and evaluated as oversize.
4. _____ The diameter of a hole that’s measured with
calipers and expressed as .7253 in.
5. _____ An angle of taper that’s expressed as 42.75°.
Var
Att
Att
Var
Var
Types of Control Charts
to variables data or attributes data.
1. _____ A slot that has a measured depth of 1.513 in.
2. _____ The smoothness of a milled surface that’s
evaluated as acceptable or unacceptable.
3. _____ The diameter of a hole that’s measured with
plug gages and evaluated as oversize.
4. _____ The diameter of a hole that’s measured with
calipers and expressed as .7253 in.
5. _____ An angle of taper that’s expressed as 42.75°.
Var
Att
Att
Var
Var
Types of Control Charts
p Chart
np Chart
C Chart
u Chart
Control Charts
Variables Attributes
Types of Control Charts
–R Chart
–s Chart X X
X –MRChart
np Chart
C Chart
u Chart
Control Charts
Variables Attributes
Types of Control Charts
–R Chart
–s Chart X X
X –MRChart
Constructing A Control Chart
Select the Process and identify the CTQ Parameter(s)
Decide on the Type of Inspection / Testing
Decide on the Type of Control Chart
Select the Process and identify the CTQ Parameter(s)
Decide on the Type of Inspection / Testing
Decide on the Type of Control Chart
DATA
TYPE
Start
Sample
Size, n
Measurable
Variables Data
X-bar
MR Chart
n = 1
Range or
S.D
X-bar -
R Chart
Range,
if n<10
Defectives
or
Defects?
Countable
Attributes Data
Constant
‘n’
Yes
np or p
Chart
Constant
‘n’
c or u
Chart
Yes
Defects
Defectives
No
p
Chart
X-bar -
sChart
S.D,
if n>10
u
Chart
No
n > 1
Control Chart Selection
TYPE
Start
Sample
Size, n
Measurable
Variables Data
X-bar
MR Chart
n = 1
Range or
S.D
X-bar -
R Chart
Range,
if n<10
Defectives
or
Defects?
Countable
Attributes Data
Constant
‘n’
Yes
np or p
Chart
Constant
‘n’
c or u
Chart
Yes
Defects
Defectives
No
p
Chart
X-bar -
sChart
S.D,
if n>10
u
Chart
No
n > 1
Control Chart Selection
Normal Distribution
•The most important continuous probability distribution in statistics is
the normal distribution
•Bell Shaped
•Symmetrical: Mean = Median = Mode
50% 50%
Measurement
•The most important continuous probability distribution in statistics is
the normal distribution
•Bell Shaped
•Symmetrical: Mean = Median = Mode
50% 50%
Measurement
m−1s m+1sm+2sm+3sm−2sm−3s m
68.27%
95.45%
99.73%
m+4sm−4s
99.99%
68.27%of the Population
falls between the
–1sand +1s.
95.45%of the Population
falls between the
–2sand +2s.
99.73%of the Population
falls between the
–3sand +3s.
etc.
If the data is Normal,
we can make calculations
that will predict the output
of the process to the
Customer. A measure of
this prediction is the
percentages of Good Product
vs. Bad Product.
49
Normal Distribution
68.27%
95.45%
99.73%
m+4sm−4s
99.99%
68.27%of the Population
falls between the
–1sand +1s.
95.45%of the Population
falls between the
–2sand +2s.
99.73%of the Population
falls between the
–3sand +3s.
etc.
If the data is Normal,
we can make calculations
that will predict the output
of the process to the
Customer. A measure of
this prediction is the
percentages of Good Product
vs. Bad Product.
49
Normal Distribution
Introduction to X-R Charts
50
50
Construction of X-R Charts2010Subgroup0
74.015
74.005
73.995
73.985
S
a
m
p
le
M
e
a
n
X=74.00
3.0SL=74.01
-3.0SL=73.99
0.05
0.04
0.03
0.02
0.01
0.00
S
a
m
p
le
R
a
n
g
e
R=0.02235
3.0SL=0.04726
-3.0SL=0.000
X-bar-R Charts
74.015
74.005
73.995
73.985
S
a
m
p
le
M
e
a
n
X=74.00
3.0SL=74.01
-3.0SL=73.99
0.05
0.04
0.03
0.02
0.01
0.00
S
a
m
p
le
R
a
n
g
e
R=0.02235
3.0SL=0.04726
-3.0SL=0.000
X-bar-R Charts
The Center Line and Control Limits of a X-chart:
The Center Line and Control Limits of a R-chart:XX2
X
XX2
3RAXLCL
XLineCenter
3RAXUCL
s−m−=
m=
s+m+= R3
R4
3RRDLCL
RLineCenter
3RRDUCL
s−=
=
s+=
Construction of X-R Charts
The Center Line and Control Limits of a R-chart:XX2
X
XX2
3RAXLCL
XLineCenter
3RAXUCL
s−m−=
m=
s+m+= R3
R4
3RRDLCL
RLineCenter
3RRDUCL
s−=
=
s+=
Construction of X-R Charts
n A2 A3 d2 c4 B3 B4 D3 D4
2 1.880 2.659 1.128 0.7979 0 3.267 0 3.267
3 1.023 1.954 1.693 0.8862 0 2.568 0 2.575
4 0.729 1.628 2.059 0.9213 0 2.266 0 2.282
5 0.577 1.427 2.326 0.9400 0 2.089 0 2.115
6 0.483 1.287 2.534 0.9515 0.030 1.970 0 2.004
7 0.419 1.182 2.704 0.9594 0.118 1.882 0.076 1.924
8 0.373 1.099 2.847 0.9650 0.185 1.815 0.136 1.864
9 0.337 1.032 2.970 0.9693 0.239 1.761 0.184 1.816
10 0.308 0.975 3.078 0.9727 0.284 1.716 0.223 1.777
11 0.285 0.927 3.173 0.9754 0.321 1.679 0.256 1.744
12 0.266 0.886 3.258 0.9776 0.354 1.646 0.283 1.717
13 0.249 0.850 3.336 0.9794 0.382 1.618 0.307 1.693
14 0.235 0.817 3.407 0.9810 0.406 1.594 0.328 1.672
15 0.223 0.789 3.472 0.9823 0.428 1.572 0.347 1.653
16 0.212 0.763 3.532 0.9835 0.448 1.552 0.363 1.637
17 0.203 0.739 3.588 0.9845 0.466 1.534 0.378 1.622
18 0.194 0.718 3.640 0.9854 0.482 1.518 0.391 1.608
19 0.187 0.698 3.689 0.9862 0.497 1.503 0.403 1.597
20 0.180 0.680 3.735 0.0969 0.510 1.490 0.415 1.585
21 0.173 0.663 3.778 0.9876 0.523 1.477 0.425 1.575
22 0.167 0.647 3.819 0.9882 0.534 1.466 0.434 1.566
23 0.162 0.633 3.858 0.9887 0.545 1.455 0.443 1.557
24 0.157 0.619 3.895 0.9892 0.555 1.445 0.451 1.548
25 0.153 0.606 3.931 0.9896 0.565 1.435 0.459 1.541 For sample size n > 10, R loses its
efficiency in estimating process sigma
and R-chart may not be appropriate.
Shewhart Constants
Construction of X-R Charts
2 1.880 2.659 1.128 0.7979 0 3.267 0 3.267
3 1.023 1.954 1.693 0.8862 0 2.568 0 2.575
4 0.729 1.628 2.059 0.9213 0 2.266 0 2.282
5 0.577 1.427 2.326 0.9400 0 2.089 0 2.115
6 0.483 1.287 2.534 0.9515 0.030 1.970 0 2.004
7 0.419 1.182 2.704 0.9594 0.118 1.882 0.076 1.924
8 0.373 1.099 2.847 0.9650 0.185 1.815 0.136 1.864
9 0.337 1.032 2.970 0.9693 0.239 1.761 0.184 1.816
10 0.308 0.975 3.078 0.9727 0.284 1.716 0.223 1.777
11 0.285 0.927 3.173 0.9754 0.321 1.679 0.256 1.744
12 0.266 0.886 3.258 0.9776 0.354 1.646 0.283 1.717
13 0.249 0.850 3.336 0.9794 0.382 1.618 0.307 1.693
14 0.235 0.817 3.407 0.9810 0.406 1.594 0.328 1.672
15 0.223 0.789 3.472 0.9823 0.428 1.572 0.347 1.653
16 0.212 0.763 3.532 0.9835 0.448 1.552 0.363 1.637
17 0.203 0.739 3.588 0.9845 0.466 1.534 0.378 1.622
18 0.194 0.718 3.640 0.9854 0.482 1.518 0.391 1.608
19 0.187 0.698 3.689 0.9862 0.497 1.503 0.403 1.597
20 0.180 0.680 3.735 0.0969 0.510 1.490 0.415 1.585
21 0.173 0.663 3.778 0.9876 0.523 1.477 0.425 1.575
22 0.167 0.647 3.819 0.9882 0.534 1.466 0.434 1.566
23 0.162 0.633 3.858 0.9887 0.545 1.455 0.443 1.557
24 0.157 0.619 3.895 0.9892 0.555 1.445 0.451 1.548
25 0.153 0.606 3.931 0.9896 0.565 1.435 0.459 1.541 For sample size n > 10, R loses its
efficiency in estimating process sigma
and R-chart may not be appropriate.
Shewhart Constants
Construction of X-R Charts
Basic steps for Process Improvement through Control charts
1.Complete preparatory steps
2.Data collection
3.Making Trial Control Limits and charting
4.Validation of Control Limits
5.Process capability study
6.Ongoing control
7.Improvement
Control Charts
54
1.Complete preparatory steps
2.Data collection
3.Making Trial Control Limits and charting
4.Validation of Control Limits
5.Process capability study
6.Ongoing control
7.Improvement
Control Charts
54
Preparatory
Steps
Ensure Level-1
control
Process
Understanding
Suitable
Environment
ControlChart-PreparatorySteps
55
Verify
Measurement
System
Steps
Ensure Level-1
control
Process
Understanding
Suitable
Environment
ControlChart-PreparatorySteps
55
Verify
Measurement
System
1. Create a suitable ( conducive ) environment
➢A key step for converting control chart from wall paper to an effective
process control tool
•Mass awareness
•Basic statistical concepts to all process engineers
56
ControlChart-PreparatorySteps
➢A key step for converting control chart from wall paper to an effective
process control tool
•Mass awareness
•Basic statistical concepts to all process engineers
56
ControlChart-PreparatorySteps
2. Understanding of Process
➢Control charts are the tool to monitor if the process is running under
common cause variation.
➢An assignable cause can enter through various factors around the process
➢A process engineer , therefore, must understand
▪What is the flow
▪What are intended outputs
▪What are inputs-controllable / Non-controllable
▪What can go wrong
▪What are the controls
57
ControlChart-PreparatorySteps
➢Control charts are the tool to monitor if the process is running under
common cause variation.
➢An assignable cause can enter through various factors around the process
➢A process engineer , therefore, must understand
▪What is the flow
▪What are intended outputs
▪What are inputs-controllable / Non-controllable
▪What can go wrong
▪What are the controls
57
ControlChart-PreparatorySteps
3. Verify Measurement System Capability
➢In SPC , all decision are based on data generated from the process.
➢What if
▪Data is not reliable
▪Measurement system is not capable of generating correct data
➢An effective MSA study is must
58
ControlChart-PreparatorySteps
➢In SPC , all decision are based on data generated from the process.
➢What if
▪Data is not reliable
▪Measurement system is not capable of generating correct data
➢An effective MSA study is must
58
ControlChart-PreparatorySteps
4 . Ensure Level-1 Control
➢SPC is a Level-2 control on a process.
➢Certain controls on the process are needed even without SPC
▪Compliance to Control plan /SOP
▪Qualified Operator
▪Other inputs control
▪Prevent un-necessary variation / over adjustment
59
ControlChart-PreparatorySteps
➢SPC is a Level-2 control on a process.
➢Certain controls on the process are needed even without SPC
▪Compliance to Control plan /SOP
▪Qualified Operator
▪Other inputs control
▪Prevent un-necessary variation / over adjustment
59
ControlChart-PreparatorySteps
60
➢Measurement must be variable
➢Situation must be practically feasible to have at least 2 measurements
in short span.
➢Mass production
➢Suitable for Product( Output) characteristics
Average-Range chart
➢Measurement must be variable
➢Situation must be practically feasible to have at least 2 measurements
in short span.
➢Mass production
➢Suitable for Product( Output) characteristics
Average-Range chart
61
•Selection of Characteristics
•Decide Sub group size (3-9)
•Decide sub group frequency
•Decide no. of sub groups (20-25 sub groups having min. 100 observations
Data Collection
•Selection of Characteristics
•Decide Sub group size (3-9)
•Decide sub group frequency
•Decide no. of sub groups (20-25 sub groups having min. 100 observations
Data Collection
62
Selection of characteristics
•Customer requirement
•High variation characteristics
•Special characteristics
•Characteristics on which other characteristics are dependent
Data Collection
Selection of characteristics
•Customer requirement
•High variation characteristics
•Special characteristics
•Characteristics on which other characteristics are dependent
Data Collection
63
➢Variability within subgroup should be small
➢For subgroup size, consider production output rate while taking
samples from the process
➢Consider measurement cost
➢Consider measurement time
Sub group size
Data Collection
➢Variability within subgroup should be small
➢For subgroup size, consider production output rate while taking
samples from the process
➢Consider measurement cost
➢Consider measurement time
Sub group size
Data Collection
64
Subgroup Frequency
•Detect change in the Process over span of time.
•All potential changes are reflected
•For initial study, may be consecutive or a very short interval.
Data Collection
Subgroup Frequency
•Detect change in the Process over span of time.
•All potential changes are reflected
•For initial study, may be consecutive or a very short interval.
Data Collection
65
No. of Subgroups
•To incorporate Major source of variation (Generally 25 subgroups or
more containing about 100 individual measurements)
Data Collection
No. of Subgroups
•To incorporate Major source of variation (Generally 25 subgroups or
more containing about 100 individual measurements)
Data Collection
66
On a data collection sheet, called control chart sheetSECTION: PRODUCT: CHARACTERISTICS:
PERSON IN-CHARGE:
X - CHART
1 2 3 4 5 6 7 8 910111213141516171819202122232425
x-R Chart
X1
X4
X5
TIME
Events:
X2
X3
x
R
Date:
SAMPLE #
DATE
x
-Chart
R-Chart
Data Collection
On a data collection sheet, called control chart sheetSECTION: PRODUCT: CHARACTERISTICS:
PERSON IN-CHARGE:
X - CHART
1 2 3 4 5 6 7 8 910111213141516171819202122232425
x-R Chart
X1
X4
X5
TIME
Events:
X2
X3
x
R
Date:
SAMPLE #
DATE
x
-Chart
R-Chart
Data Collection
Average-Range ( )ChartX-R
1234567891011121314151617181920
1
0.650.750.750.600.700.600.750.600.650.600.800.850.700.650.900.750.750.750.650.60
2
0.700.850.800.700.750.750.700.700.800.800.700.700.650.600.550.800.650.600.700.85
3
0.650.750.800.700.650.750.650.800.850.600.900.850.750.850.800.750.850.600.850.65
4
0.650.850.700.750.850.850.650.650.750.650.700.600.600.650.650.800.600.650.700.70
5
0.850.650.750.650.800.700.800.750.750.750.650.700.700.600.850.650.800.600.700.65
X
R
Piston rings for an automotive engine are forged. 20 preliminary samples, each of size 5, were
obtained. The thickness of these rings are shown here. Verify if the forging process is in statistical
control.
1234567891011121314151617181920
1
0.650.750.750.600.700.600.750.600.650.600.800.850.700.650.900.750.750.750.650.60
2
0.700.850.800.700.750.750.700.700.800.800.700.700.650.600.550.800.650.600.700.85
3
0.650.750.800.700.650.750.650.800.850.600.900.850.750.850.800.750.850.600.850.65
4
0.650.850.700.750.850.850.650.650.750.650.700.600.600.650.650.800.600.650.700.70
5
0.850.650.750.650.800.700.800.750.750.750.650.700.700.600.850.650.800.600.700.65
X
R
Piston rings for an automotive engine are forged. 20 preliminary samples, each of size 5, were
obtained. The thickness of these rings are shown here. Verify if the forging process is in statistical
control.
68
•Calculate Average of each Subgroup
X = ( X
1 + X
2 + … + X
n)/ n
•Calculate Range of each Subgroup
R = X
max. -X
min.
•Calculate Process average ( Overall average)
=(X
1+ X
2+ … + X
k)/ k
•Calculate Average Range
R= (R
1+ R
2+ … + R
k)/ k
❖X
1, X
2,…., X
nare individual values within the subgroup
❖n is the Subgroup Sample Size
❖k = No. of Subgroups
X
Establish Control Limits
•Calculate Average of each Subgroup
X = ( X
1 + X
2 + … + X
n)/ n
•Calculate Range of each Subgroup
R = X
max. -X
min.
•Calculate Process average ( Overall average)
=(X
1+ X
2+ … + X
k)/ k
•Calculate Average Range
R= (R
1+ R
2+ … + R
k)/ k
❖X
1, X
2,…., X
nare individual values within the subgroup
❖n is the Subgroup Sample Size
❖k = No. of Subgroups
X
Establish Control Limits
Average-Range ( )ChartX-R
1234567891011121314151617181920
1
0.650.750.750.600.700.600.750.600.650.600.800.850.700.650.900.750.750.750.650.60
2
0.700.850.800.700.750.750.700.700.800.800.700.700.650.600.550.800.650.600.700.85
3
0.650.750.800.700.650.750.650.800.850.600.900.850.750.850.800.750.850.600.850.65
4
0.650.850.700.750.850.850.650.650.750.650.700.600.600.650.650.800.600.650.700.70
5
0.850.650.750.650.800.700.800.750.750.750.650.700.700.600.850.650.800.600.700.65
X
0.700.770.760.680.750.730.710.700.760.680.750.740.680.670.750.750.730.640.720.69
R
0.200.200.100.150.200.250.150.200.200.200.250.250.150.250.350.150.250.150.200.25
1234567891011121314151617181920
1
0.650.750.750.600.700.600.750.600.650.600.800.850.700.650.900.750.750.750.650.60
2
0.700.850.800.700.750.750.700.700.800.800.700.700.650.600.550.800.650.600.700.85
3
0.650.750.800.700.650.750.650.800.850.600.900.850.750.850.800.750.850.600.850.65
4
0.650.850.700.750.850.850.650.650.750.650.700.600.600.650.650.800.600.650.700.70
5
0.850.650.750.650.800.700.800.750.750.750.650.700.700.600.850.650.800.600.700.65
X
0.700.770.760.680.750.730.710.700.760.680.750.740.680.670.750.750.730.640.720.69
R
0.200.200.100.150.200.250.150.200.200.200.250.250.150.250.350.150.250.150.200.25
70
•Calculate Trial Control Limits for Range Chart
UCL
R= D
4 R
LCL
R = D
3R
.
•Calculate Trial Control Limits for Average Chart
UCL
X=+ A
2 R
LCL
X = -A
2 R
D
4, D
3and A
2are constant varying as per sample size (n).
X
Establish Control Limits
X
•Calculate Trial Control Limits for Range Chart
UCL
R= D
4 R
LCL
R = D
3R
.
•Calculate Trial Control Limits for Average Chart
UCL
X=+ A
2 R
LCL
X = -A
2 R
D
4, D
3and A
2are constant varying as per sample size (n).
X
Establish Control Limits
X
71
Table Of ConstantsSubgroup
Size (n)
A2 d2 D3 D4 E2
2 1.880 1.128 - 3.267 2.660
3 1.023 1.693 - 2.574 1.772
4 0.729 2.059 - 2.282 1.457
5 0.577 2.326 - 2.114 1.290
6 0.483 2.534 - 2.004 1.184
7 0.419 2.704 0.076 1.924 1.109
8 0.373 2.847 0.136 1.864 1.054
9 0.337 2.970 0.184 1.816 1.010
Establish Control Limits
Table Of ConstantsSubgroup
Size (n)
A2 d2 D3 D4 E2
2 1.880 1.128 - 3.267 2.660
3 1.023 1.693 - 2.574 1.772
4 0.729 2.059 - 2.282 1.457
5 0.577 2.326 - 2.114 1.290
6 0.483 2.534 - 2.004 1.184
7 0.419 2.704 0.076 1.924 1.109
8 0.373 2.847 0.136 1.864 1.054
9 0.337 2.970 0.184 1.816 1.010
Establish Control Limits
X double bar 0.718
R bar 0.21
For Average Control Chart
UCL 0.837
LCL 0.60
For Range Control Chart
UCL 0.443
LCL 0
72
Establish Control Limits
R bar 0.21
For Average Control Chart
UCL 0.837
LCL 0.60
For Range Control Chart
UCL 0.443
LCL 0
72
Establish Control Limits
73
Draw Range ChartR-Chart
0.00
0.20
0.40
0.60
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
UCL R-Bar LCL Range
R-chart measures
variability within
samples
Draw Range ChartR-Chart
0.00
0.20
0.40
0.60
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
UCL R-Bar LCL Range
R-chart measures
variability within
samples
74X-Bar Chart
0.50
0.60
0.70
0.80
1.002.003.004.005.006.007.008.009.0010.0011.0012.0013.0014.0015.0016.0017.0018.0019.0020.00
UCL LCL AVERAGE X Average
Draw Average Chart
X-chart measures
variability between
samples
0.50
0.60
0.70
0.80
1.002.003.004.005.006.007.008.009.0010.0011.0012.0013.0014.0015.0016.0017.0018.0019.0020.00
UCL LCL AVERAGE X Average
Draw Average Chart
X-chart measures
variability between
samples
75
Validation of Control Limits
Validation of Control Limits
➢Control limits should indicate the variation due to common causes only.
➢Hence it should be based on data where there is no special cause.
➢Any control limit based on special cause data can not be considered reliable
Validation of Control limits
76
What to do?
➢Hence it should be based on data where there is no special cause.
➢Any control limit based on special cause data can not be considered reliable
Validation of Control limits
76
What to do?
Validation of control limits for initial control charts
➢Identify any out of control or special cause situation( point above UCL & below LCL)-Start from R chart
➢Discard that sub group showing out of control situation.
➢Recalculate control limits for average & range, plot the charts and again analyze for any out of control
situation
➢Re-discard if any any out of control situation again found. Continue till all plots indicate a control
situation.
➢Repeat same exercise with Average Chart
➢If more than 50% data are required to be discarded, reject all data and recollect.
➢Once initial control chart indicates control situation
▪ Calculate Initial capability
▪ Extend control limits for ongoing control
77
Validation of Control limits
➢Identify any out of control or special cause situation( point above UCL & below LCL)-Start from R chart
➢Discard that sub group showing out of control situation.
➢Recalculate control limits for average & range, plot the charts and again analyze for any out of control
situation
➢Re-discard if any any out of control situation again found. Continue till all plots indicate a control
situation.
➢Repeat same exercise with Average Chart
➢If more than 50% data are required to be discarded, reject all data and recollect.
➢Once initial control chart indicates control situation
▪ Calculate Initial capability
▪ Extend control limits for ongoing control
77
Validation of Control limits
A Process is in Control if
•No sample points outside limits
•Most points near process average
•About equal # points above & below centerline
•Points appear randomly distributed
Interpretation of Control Charts
•No sample points outside limits
•Most points near process average
•About equal # points above & below centerline
•Points appear randomly distributed
Interpretation of Control Charts
Validation of Control limits-ExampleSub-
Group No.
Sample 1 Sample 2 Sample 3 Sample 4
Sub-Group
Average
Range
1 4.90 4.80 5.10 5.40 5.050 0.60
2 5.00 5.80 5.30 5.30 5.350 0.80
3 4.40 4.70 4.80 4.60 4.625 0.40
4 4.60 5.80 5.40 4.90 5.175 1.20
5 5.20 5.30 6.10 5.20 5.450 0.90
6 5.00 5.90 5.80 4.80 5.375 1.10
7 4.30 4.60 4.70 4.50 4.525 0.40
8 4.90 4.90 5.50 5.70 5.250 0.80
9 5.90 6.40 6.10 6.50 6.225 0.60
10 5.30 5.90 6.10 4.80 5.525 1.30
11 4.60 4.60 5.30 5.00 4.875 0.70
12 5.30 5.80 5.40 5.10 5.400 0.70
13 4.90 5.30 5.20 5.70 5.275 0.80
14 5.20 5.40 4.60 5.50 5.175 0.90
15 5.40 4.80 4.20 5.10 4.875 1.20
16 4.60 4.40 4.90 5.10 4.750 0.70
17 5.70 5.40 5.00 4.80 5.225 0.90
18 5.10 4.30 5.70 6.50 5.400 2.20
19 5.90 6.40 6.20 6.10 6.150 0.50
20 5.00 5.10 4.50 4.80 4.850 0.60
21 4.90 5.90 5.30 5.20 5.325 1.00
22 5.40 5.90 4.40 5.00 5.175 1.50
23 5.20 4.70 5.70 5.80 5.350 1.10
24 4.00 4.80 5.10 6.10 5.000 2.10
25 5.30 5.80 6.00 6.30 5.850 1.00
5.249 0.960Average Sub-
Group No.
Sample 1 Sample 2 Sample 3 Sample 4
Sub-Group
Average
Range
1 4.90 4.80 5.10 5.40 5.050 0.60
2 5.00 5.80 5.30 5.30 5.350 0.80
3 4.40 4.70 4.80 4.60 4.625 0.40
4 4.60 5.80 5.40 4.90 5.175 1.20
5 5.20 5.30 6.10 5.20 5.450 0.90
6 5.00 5.90 5.80 4.80 5.375 1.10
7 4.30 4.60 4.70 4.50 4.525 0.40
8 4.90 4.90 5.50 5.70 5.250 0.80
9 5.90 6.40 6.10 6.50 6.225 0.60
10 5.30 5.90 6.10 4.80 5.525 1.30
11 4.60 4.60 5.30 5.00 4.875 0.70
12 5.30 5.80 5.40 5.10 5.400 0.70
13 4.90 5.30 5.20 5.70 5.275 0.80
14 5.20 5.40 4.60 5.50 5.175 0.90
15 5.40 4.80 4.20 5.10 4.875 1.20
16 4.60 4.40 4.90 5.10 4.750 0.70
17 5.70 5.40 5.00 4.80 5.225 0.90
18 5.10 4.30 5.70 6.50 5.400 2.20
19 5.90 6.40 6.20 6.10 6.150 0.50
20 5.00 5.10 4.50 4.80 4.850 0.60
21 4.90 5.90 5.30 5.20 5.325 1.00
22 5.40 5.90 4.40 5.00 5.175 1.50
23 5.20 4.70 5.70 5.80 5.350 1.10
24 4.00 4.80 5.10 6.10 5.000 2.10
25 5.30 5.80 6.00 6.30 5.850 1.00
5.249 0.960Average Sub-
Group No.
Sample 1 Sample 2 Sample 3 Sample 4
Sub-Group
Average
Range
1 4.90 4.80 5.10 5.40 5.050 0.60
2 5.00 5.80 5.30 5.30 5.350 0.80
3 4.40 4.70 4.80 4.60 4.625 0.40
4 4.60 5.80 5.40 4.90 5.175 1.20
5 5.20 5.30 6.10 5.20 5.450 0.90
6 5.00 5.90 5.80 4.80 5.375 1.10
7 4.30 4.60 4.70 4.50 4.525 0.40
8 4.90 4.90 5.50 5.70 5.250 0.80
9 5.90 6.40 6.10 6.50 6.225 0.60
10 5.30 5.90 6.10 4.80 5.525 1.30
11 4.60 4.60 5.30 5.00 4.875 0.70
12 5.30 5.80 5.40 5.10 5.400 0.70
13 4.90 5.30 5.20 5.70 5.275 0.80
14 5.20 5.40 4.60 5.50 5.175 0.90
15 5.40 4.80 4.20 5.10 4.875 1.20
16 4.60 4.40 4.90 5.10 4.750 0.70
17 5.70 5.40 5.00 4.80 5.225 0.90
18 5.10 4.30 5.70 6.50 5.400 2.20
19 5.90 6.40 6.20 6.10 6.150 0.50
20 5.00 5.10 4.50 4.80 4.850 0.60
21 4.90 5.90 5.30 5.20 5.325 1.00
22 5.40 5.90 4.40 5.00 5.175 1.50
23 5.20 4.70 5.70 5.80 5.350 1.10
24 4.00 4.80 5.10 6.10 5.000 2.10
25 5.30 5.80 6.00 6.30 5.850 1.00
5.249 0.960Average Sub-
Group No.
Sample 1 Sample 2 Sample 3 Sample 4
Sub-Group
Average
Range
1 4.90 4.80 5.10 5.40 5.050 0.60
2 5.00 5.80 5.30 5.30 5.350 0.80
3 4.40 4.70 4.80 4.60 4.625 0.40
4 4.60 5.80 5.40 4.90 5.175 1.20
5 5.20 5.30 6.10 5.20 5.450 0.90
6 5.00 5.90 5.80 4.80 5.375 1.10
7 4.30 4.60 4.70 4.50 4.525 0.40
8 4.90 4.90 5.50 5.70 5.250 0.80
9 5.90 6.40 6.10 6.50 6.225 0.60
10 5.30 5.90 6.10 4.80 5.525 1.30
11 4.60 4.60 5.30 5.00 4.875 0.70
12 5.30 5.80 5.40 5.10 5.400 0.70
13 4.90 5.30 5.20 5.70 5.275 0.80
14 5.20 5.40 4.60 5.50 5.175 0.90
15 5.40 4.80 4.20 5.10 4.875 1.20
16 4.60 4.40 4.90 5.10 4.750 0.70
17 5.70 5.40 5.00 4.80 5.225 0.90
18 5.10 4.30 5.70 6.50 5.400 2.20
19 5.90 6.40 6.20 6.10 6.150 0.50
20 5.00 5.10 4.50 4.80 4.850 0.60
21 4.90 5.90 5.30 5.20 5.325 1.00
22 5.40 5.90 4.40 5.00 5.175 1.50
23 5.20 4.70 5.70 5.80 5.350 1.10
24 4.00 4.80 5.10 6.10 5.000 2.10
25 5.30 5.80 6.00 6.30 5.850 1.00
5.249 0.960Average
Group No.
Sample 1 Sample 2 Sample 3 Sample 4
Sub-Group
Average
Range
1 4.90 4.80 5.10 5.40 5.050 0.60
2 5.00 5.80 5.30 5.30 5.350 0.80
3 4.40 4.70 4.80 4.60 4.625 0.40
4 4.60 5.80 5.40 4.90 5.175 1.20
5 5.20 5.30 6.10 5.20 5.450 0.90
6 5.00 5.90 5.80 4.80 5.375 1.10
7 4.30 4.60 4.70 4.50 4.525 0.40
8 4.90 4.90 5.50 5.70 5.250 0.80
9 5.90 6.40 6.10 6.50 6.225 0.60
10 5.30 5.90 6.10 4.80 5.525 1.30
11 4.60 4.60 5.30 5.00 4.875 0.70
12 5.30 5.80 5.40 5.10 5.400 0.70
13 4.90 5.30 5.20 5.70 5.275 0.80
14 5.20 5.40 4.60 5.50 5.175 0.90
15 5.40 4.80 4.20 5.10 4.875 1.20
16 4.60 4.40 4.90 5.10 4.750 0.70
17 5.70 5.40 5.00 4.80 5.225 0.90
18 5.10 4.30 5.70 6.50 5.400 2.20
19 5.90 6.40 6.20 6.10 6.150 0.50
20 5.00 5.10 4.50 4.80 4.850 0.60
21 4.90 5.90 5.30 5.20 5.325 1.00
22 5.40 5.90 4.40 5.00 5.175 1.50
23 5.20 4.70 5.70 5.80 5.350 1.10
24 4.00 4.80 5.10 6.10 5.000 2.10
25 5.30 5.80 6.00 6.30 5.850 1.00
5.249 0.960Average Sub-
Group No.
Sample 1 Sample 2 Sample 3 Sample 4
Sub-Group
Average
Range
1 4.90 4.80 5.10 5.40 5.050 0.60
2 5.00 5.80 5.30 5.30 5.350 0.80
3 4.40 4.70 4.80 4.60 4.625 0.40
4 4.60 5.80 5.40 4.90 5.175 1.20
5 5.20 5.30 6.10 5.20 5.450 0.90
6 5.00 5.90 5.80 4.80 5.375 1.10
7 4.30 4.60 4.70 4.50 4.525 0.40
8 4.90 4.90 5.50 5.70 5.250 0.80
9 5.90 6.40 6.10 6.50 6.225 0.60
10 5.30 5.90 6.10 4.80 5.525 1.30
11 4.60 4.60 5.30 5.00 4.875 0.70
12 5.30 5.80 5.40 5.10 5.400 0.70
13 4.90 5.30 5.20 5.70 5.275 0.80
14 5.20 5.40 4.60 5.50 5.175 0.90
15 5.40 4.80 4.20 5.10 4.875 1.20
16 4.60 4.40 4.90 5.10 4.750 0.70
17 5.70 5.40 5.00 4.80 5.225 0.90
18 5.10 4.30 5.70 6.50 5.400 2.20
19 5.90 6.40 6.20 6.10 6.150 0.50
20 5.00 5.10 4.50 4.80 4.850 0.60
21 4.90 5.90 5.30 5.20 5.325 1.00
22 5.40 5.90 4.40 5.00 5.175 1.50
23 5.20 4.70 5.70 5.80 5.350 1.10
24 4.00 4.80 5.10 6.10 5.000 2.10
25 5.30 5.80 6.00 6.30 5.850 1.00
5.249 0.960Average Sub-
Group No.
Sample 1 Sample 2 Sample 3 Sample 4
Sub-Group
Average
Range
1 4.90 4.80 5.10 5.40 5.050 0.60
2 5.00 5.80 5.30 5.30 5.350 0.80
3 4.40 4.70 4.80 4.60 4.625 0.40
4 4.60 5.80 5.40 4.90 5.175 1.20
5 5.20 5.30 6.10 5.20 5.450 0.90
6 5.00 5.90 5.80 4.80 5.375 1.10
7 4.30 4.60 4.70 4.50 4.525 0.40
8 4.90 4.90 5.50 5.70 5.250 0.80
9 5.90 6.40 6.10 6.50 6.225 0.60
10 5.30 5.90 6.10 4.80 5.525 1.30
11 4.60 4.60 5.30 5.00 4.875 0.70
12 5.30 5.80 5.40 5.10 5.400 0.70
13 4.90 5.30 5.20 5.70 5.275 0.80
14 5.20 5.40 4.60 5.50 5.175 0.90
15 5.40 4.80 4.20 5.10 4.875 1.20
16 4.60 4.40 4.90 5.10 4.750 0.70
17 5.70 5.40 5.00 4.80 5.225 0.90
18 5.10 4.30 5.70 6.50 5.400 2.20
19 5.90 6.40 6.20 6.10 6.150 0.50
20 5.00 5.10 4.50 4.80 4.850 0.60
21 4.90 5.90 5.30 5.20 5.325 1.00
22 5.40 5.90 4.40 5.00 5.175 1.50
23 5.20 4.70 5.70 5.80 5.350 1.10
24 4.00 4.80 5.10 6.10 5.000 2.10
25 5.30 5.80 6.00 6.30 5.850 1.00
5.249 0.960Average Sub-
Group No.
Sample 1 Sample 2 Sample 3 Sample 4
Sub-Group
Average
Range
1 4.90 4.80 5.10 5.40 5.050 0.60
2 5.00 5.80 5.30 5.30 5.350 0.80
3 4.40 4.70 4.80 4.60 4.625 0.40
4 4.60 5.80 5.40 4.90 5.175 1.20
5 5.20 5.30 6.10 5.20 5.450 0.90
6 5.00 5.90 5.80 4.80 5.375 1.10
7 4.30 4.60 4.70 4.50 4.525 0.40
8 4.90 4.90 5.50 5.70 5.250 0.80
9 5.90 6.40 6.10 6.50 6.225 0.60
10 5.30 5.90 6.10 4.80 5.525 1.30
11 4.60 4.60 5.30 5.00 4.875 0.70
12 5.30 5.80 5.40 5.10 5.400 0.70
13 4.90 5.30 5.20 5.70 5.275 0.80
14 5.20 5.40 4.60 5.50 5.175 0.90
15 5.40 4.80 4.20 5.10 4.875 1.20
16 4.60 4.40 4.90 5.10 4.750 0.70
17 5.70 5.40 5.00 4.80 5.225 0.90
18 5.10 4.30 5.70 6.50 5.400 2.20
19 5.90 6.40 6.20 6.10 6.150 0.50
20 5.00 5.10 4.50 4.80 4.850 0.60
21 4.90 5.90 5.30 5.20 5.325 1.00
22 5.40 5.90 4.40 5.00 5.175 1.50
23 5.20 4.70 5.70 5.80 5.350 1.10
24 4.00 4.80 5.10 6.10 5.000 2.10
25 5.30 5.80 6.00 6.30 5.850 1.00
5.249 0.960Average
0.00
0.50
1.00
1.50
2.00
2.50
12345678910111213141516171819202122232425
Sub-GroupNo.
Range
'R' Chart
2.191
0.960
0.000
Validation of Control limits-Example
0.50
1.00
1.50
2.00
2.50
12345678910111213141516171819202122232425
Sub-GroupNo.
Range
'R' Chart
2.191
0.960
0.000
Validation of Control limits-Example
Sub-
Group No.
Sample 1 Sample 2 Sample 3 Sample 4
Sub-Group
Average
Range
1 4.90 4.80 5.10 5.40 5.050 0.60
2 5.00 5.80 5.30 5.30 5.350 0.80
3 4.40 4.70 4.80 4.60 4.625 0.40
4 4.60 5.80 5.40 4.90 5.175 1.20
5 5.20 5.30 6.10 5.20 5.450 0.90
6 5.00 5.90 5.80 4.80 5.375 1.10
7 4.30 4.60 4.70 4.50 4.525 0.40
8 4.90 4.90 5.50 5.70 5.250 0.80
9 5.90 6.40 6.10 6.50 6.225 0.60
10 5.30 5.90 6.10 4.80 5.525 1.30
11 4.60 4.60 5.30 5.00 4.875 0.70
12 5.30 5.80 5.40 5.10 5.400 0.70
13 4.90 5.30 5.20 5.70 5.275 0.80
14 5.20 5.40 4.60 5.50 5.175 0.90
15 5.40 4.80 4.20 5.10 4.875 1.20
16 4.60 4.40 4.90 5.10 4.750 0.70
17 5.70 5.40 5.00 4.80 5.225 0.90
18 5.10 4.30 5.70 6.50 5.400 2.20
19 5.90 6.40 6.20 6.10 6.150 0.50
20 5.00 5.10 4.50 4.80 4.850 0.60
21 4.90 5.90 5.30 5.20 5.325 1.00
22 5.40 5.90 4.40 5.00 5.175 1.50
23 5.20 4.70 5.70 5.80 5.350 1.10
24 4.00 4.80 5.10 6.10 5.000 2.10
25 5.30 5.80 6.00 6.30 5.850 1.00
5.249 0.960Average Sub-
Group No.
Sample 1 Sample 2 Sample 3 Sample 4
Sub-Group
Average
Range
1 4.90 4.80 5.10 5.40 5.050 0.60
2 5.00 5.80 5.30 5.30 5.350 0.80
3 4.40 4.70 4.80 4.60 4.625 0.40
4 4.60 5.80 5.40 4.90 5.175 1.20
5 5.20 5.30 6.10 5.20 5.450 0.90
6 5.00 5.90 5.80 4.80 5.375 1.10
7 4.30 4.60 4.70 4.50 4.525 0.40
8 4.90 4.90 5.50 5.70 5.250 0.80
9 5.90 6.40 6.10 6.50 6.225 0.60
10 5.30 5.90 6.10 4.80 5.525 1.30
11 4.60 4.60 5.30 5.00 4.875 0.70
12 5.30 5.80 5.40 5.10 5.400 0.70
13 4.90 5.30 5.20 5.70 5.275 0.80
14 5.20 5.40 4.60 5.50 5.175 0.90
15 5.40 4.80 4.20 5.10 4.875 1.20
16 4.60 4.40 4.90 5.10 4.750 0.70
17 5.70 5.40 5.00 4.80 5.225 0.90
18 5.10 4.30 5.70 6.50 5.400 2.20
19 5.90 6.40 6.20 6.10 6.150 0.50
20 5.00 5.10 4.50 4.80 4.850 0.60
21 4.90 5.90 5.30 5.20 5.325 1.00
22 5.40 5.90 4.40 5.00 5.175 1.50
23 5.20 4.70 5.70 5.80 5.350 1.10
24 4.00 4.80 5.10 6.10 5.000 2.10
25 5.30 5.80 6.00 6.30 5.850 1.00
5.253 0.857Average Validation of Control limits-Example
Group No.
Sample 1 Sample 2 Sample 3 Sample 4
Sub-Group
Average
Range
1 4.90 4.80 5.10 5.40 5.050 0.60
2 5.00 5.80 5.30 5.30 5.350 0.80
3 4.40 4.70 4.80 4.60 4.625 0.40
4 4.60 5.80 5.40 4.90 5.175 1.20
5 5.20 5.30 6.10 5.20 5.450 0.90
6 5.00 5.90 5.80 4.80 5.375 1.10
7 4.30 4.60 4.70 4.50 4.525 0.40
8 4.90 4.90 5.50 5.70 5.250 0.80
9 5.90 6.40 6.10 6.50 6.225 0.60
10 5.30 5.90 6.10 4.80 5.525 1.30
11 4.60 4.60 5.30 5.00 4.875 0.70
12 5.30 5.80 5.40 5.10 5.400 0.70
13 4.90 5.30 5.20 5.70 5.275 0.80
14 5.20 5.40 4.60 5.50 5.175 0.90
15 5.40 4.80 4.20 5.10 4.875 1.20
16 4.60 4.40 4.90 5.10 4.750 0.70
17 5.70 5.40 5.00 4.80 5.225 0.90
18 5.10 4.30 5.70 6.50 5.400 2.20
19 5.90 6.40 6.20 6.10 6.150 0.50
20 5.00 5.10 4.50 4.80 4.850 0.60
21 4.90 5.90 5.30 5.20 5.325 1.00
22 5.40 5.90 4.40 5.00 5.175 1.50
23 5.20 4.70 5.70 5.80 5.350 1.10
24 4.00 4.80 5.10 6.10 5.000 2.10
25 5.30 5.80 6.00 6.30 5.850 1.00
5.249 0.960Average Sub-
Group No.
Sample 1 Sample 2 Sample 3 Sample 4
Sub-Group
Average
Range
1 4.90 4.80 5.10 5.40 5.050 0.60
2 5.00 5.80 5.30 5.30 5.350 0.80
3 4.40 4.70 4.80 4.60 4.625 0.40
4 4.60 5.80 5.40 4.90 5.175 1.20
5 5.20 5.30 6.10 5.20 5.450 0.90
6 5.00 5.90 5.80 4.80 5.375 1.10
7 4.30 4.60 4.70 4.50 4.525 0.40
8 4.90 4.90 5.50 5.70 5.250 0.80
9 5.90 6.40 6.10 6.50 6.225 0.60
10 5.30 5.90 6.10 4.80 5.525 1.30
11 4.60 4.60 5.30 5.00 4.875 0.70
12 5.30 5.80 5.40 5.10 5.400 0.70
13 4.90 5.30 5.20 5.70 5.275 0.80
14 5.20 5.40 4.60 5.50 5.175 0.90
15 5.40 4.80 4.20 5.10 4.875 1.20
16 4.60 4.40 4.90 5.10 4.750 0.70
17 5.70 5.40 5.00 4.80 5.225 0.90
18 5.10 4.30 5.70 6.50 5.400 2.20
19 5.90 6.40 6.20 6.10 6.150 0.50
20 5.00 5.10 4.50 4.80 4.850 0.60
21 4.90 5.90 5.30 5.20 5.325 1.00
22 5.40 5.90 4.40 5.00 5.175 1.50
23 5.20 4.70 5.70 5.80 5.350 1.10
24 4.00 4.80 5.10 6.10 5.000 2.10
25 5.30 5.80 6.00 6.30 5.850 1.00
5.253 0.857Average Validation of Control limits-Example
2223
Sub-GroupNo.
123456789101112131415161718192021
4.000
4.500
5.000
5.500
6.000
6.500
Coil Dia
'R' Chart
212223
Sub-GroupNo.
Range
0.00
0.50
1.00
1.50
2.00
2.50
1234567891011121314151617181920
0.000
0.857
1.955
4.629
5.253
5.878
Validation of Control limits-Example
Sub-GroupNo.
123456789101112131415161718192021
4.000
4.500
5.000
5.500
6.000
6.500
Coil Dia
'R' Chart
212223
Sub-GroupNo.
Range
0.00
0.50
1.00
1.50
2.00
2.50
1234567891011121314151617181920
0.000
0.857
1.955
4.629
5.253
5.878
Validation of Control limits-Example
Sub-
Group No.
Sample 1 Sample 2 Sample 3 Sample 4
Sub-Group
Average
Range
1 4.90 4.80 5.10 5.40 5.050 0.60
2 5.00 5.80 5.30 5.30 5.350 0.80
3 4.40 4.70 4.80 4.60 4.625 0.40
4 4.60 5.80 5.40 4.90 5.175 1.20
5 5.20 5.30 6.10 5.20 5.450 0.90
6 5.00 5.90 5.80 4.80 5.375 1.10
7 4.30 4.60 4.70 4.50 4.525 0.40
8 4.90 4.90 5.50 5.70 5.250 0.80
9 5.90 6.40 6.10 6.50 6.225 0.60
10 5.30 5.90 6.10 4.80 5.525 1.30
11 4.60 4.60 5.30 5.00 4.875 0.70
12 5.30 5.80 5.40 5.10 5.400 0.70
13 4.90 5.30 5.20 5.70 5.275 0.80
14 5.20 5.40 4.60 5.50 5.175 0.90
15 5.40 4.80 4.20 5.10 4.875 1.20
16 4.60 4.40 4.90 5.10 4.750 0.70
17 5.70 5.40 5.00 4.80 5.225 0.90
18 5.90 6.40 6.20 6.10 6.150 0.50
19 5.00 5.10 4.50 4.80 4.850 0.60
20 4.90 5.90 5.30 5.20 5.325 1.00
21 5.40 5.90 4.40 5.00 5.175 1.50
22 5.20 4.70 5.70 5.80 5.350 1.10
23 5.30 5.80 6.00 6.30 5.850 1.00
5.253 0.857Average Sub-
Group No.
Sample 1 Sample 2 Sample 3 Sample 4
Sub-Group
Average
Range
1 4.90 4.80 5.10 5.40 5.050 0.60
2 5.00 5.80 5.30 5.30 5.350 0.80
3 4.40 4.70 4.80 4.60 4.625 0.40
4 4.60 5.80 5.40 4.90 5.175 1.20
5 5.20 5.30 6.10 5.20 5.450 0.90
6 5.00 5.90 5.80 4.80 5.375 1.10
7 4.30 4.60 4.70 4.50 4.525 0.40
8 4.90 4.90 5.50 5.70 5.250 0.80
9 5.90 6.40 6.10 6.50 6.225 0.60
10 5.30 5.90 6.10 4.80 5.525 1.30
11 4.60 4.60 5.30 5.00 4.875 0.70
12 5.30 5.80 5.40 5.10 5.400 0.70
13 4.90 5.30 5.20 5.70 5.275 0.80
14 5.20 5.40 4.60 5.50 5.175 0.90
15 5.40 4.80 4.20 5.10 4.875 1.20
16 4.60 4.40 4.90 5.10 4.750 0.70
17 5.70 5.40 5.00 4.80 5.225 0.90
18 5.10 4.30 5.70 6.50 5.400 2.20
19 5.90 6.40 6.20 6.10 6.150 0.50
20 5.00 5.10 4.50 4.80 4.850 0.60
21 4.90 5.90 5.30 5.20 5.325 1.00
22 5.40 5.90 4.40 5.00 5.175 1.50
23 5.20 4.70 5.70 5.80 5.350 1.10
24 4.00 4.80 5.10 6.10 5.000 2.10
25 5.30 5.80 6.00 6.30 5.850 1.00
5.196 0.910Average Validation of Control limits-Example
Group No.
Sample 1 Sample 2 Sample 3 Sample 4
Sub-Group
Average
Range
1 4.90 4.80 5.10 5.40 5.050 0.60
2 5.00 5.80 5.30 5.30 5.350 0.80
3 4.40 4.70 4.80 4.60 4.625 0.40
4 4.60 5.80 5.40 4.90 5.175 1.20
5 5.20 5.30 6.10 5.20 5.450 0.90
6 5.00 5.90 5.80 4.80 5.375 1.10
7 4.30 4.60 4.70 4.50 4.525 0.40
8 4.90 4.90 5.50 5.70 5.250 0.80
9 5.90 6.40 6.10 6.50 6.225 0.60
10 5.30 5.90 6.10 4.80 5.525 1.30
11 4.60 4.60 5.30 5.00 4.875 0.70
12 5.30 5.80 5.40 5.10 5.400 0.70
13 4.90 5.30 5.20 5.70 5.275 0.80
14 5.20 5.40 4.60 5.50 5.175 0.90
15 5.40 4.80 4.20 5.10 4.875 1.20
16 4.60 4.40 4.90 5.10 4.750 0.70
17 5.70 5.40 5.00 4.80 5.225 0.90
18 5.90 6.40 6.20 6.10 6.150 0.50
19 5.00 5.10 4.50 4.80 4.850 0.60
20 4.90 5.90 5.30 5.20 5.325 1.00
21 5.40 5.90 4.40 5.00 5.175 1.50
22 5.20 4.70 5.70 5.80 5.350 1.10
23 5.30 5.80 6.00 6.30 5.850 1.00
5.253 0.857Average Sub-
Group No.
Sample 1 Sample 2 Sample 3 Sample 4
Sub-Group
Average
Range
1 4.90 4.80 5.10 5.40 5.050 0.60
2 5.00 5.80 5.30 5.30 5.350 0.80
3 4.40 4.70 4.80 4.60 4.625 0.40
4 4.60 5.80 5.40 4.90 5.175 1.20
5 5.20 5.30 6.10 5.20 5.450 0.90
6 5.00 5.90 5.80 4.80 5.375 1.10
7 4.30 4.60 4.70 4.50 4.525 0.40
8 4.90 4.90 5.50 5.70 5.250 0.80
9 5.90 6.40 6.10 6.50 6.225 0.60
10 5.30 5.90 6.10 4.80 5.525 1.30
11 4.60 4.60 5.30 5.00 4.875 0.70
12 5.30 5.80 5.40 5.10 5.400 0.70
13 4.90 5.30 5.20 5.70 5.275 0.80
14 5.20 5.40 4.60 5.50 5.175 0.90
15 5.40 4.80 4.20 5.10 4.875 1.20
16 4.60 4.40 4.90 5.10 4.750 0.70
17 5.70 5.40 5.00 4.80 5.225 0.90
18 5.10 4.30 5.70 6.50 5.400 2.20
19 5.90 6.40 6.20 6.10 6.150 0.50
20 5.00 5.10 4.50 4.80 4.850 0.60
21 4.90 5.90 5.30 5.20 5.325 1.00
22 5.40 5.90 4.40 5.00 5.175 1.50
23 5.20 4.70 5.70 5.80 5.350 1.10
24 4.00 4.80 5.10 6.10 5.000 2.10
25 5.30 5.80 6.00 6.30 5.850 1.00
5.196 0.910Average Validation of Control limits-Example
'R' Chart
0.00
0.50
1.00
1.50
2.00
2.50
1234567891011121314151617181920
Sub-GroupNo.
Range
4.00
4.50
5.00
5.50
6.00
Coil Dia
891011121314151617181920
Sub-Group No.
1234567
4.533
5.196
5.860
0.000
0.910
2.077
Validation of Control limits-Example
0.00
0.50
1.00
1.50
2.00
2.50
1234567891011121314151617181920
Sub-GroupNo.
Range
4.00
4.50
5.00
5.50
6.00
Coil Dia
891011121314151617181920
Sub-Group No.
1234567
4.533
5.196
5.860
0.000
0.910
2.077
Validation of Control limits-Example
Process Capability Study
85
85
86
Process Capability
When Calculate Process Capability ?
•All the Assignable Causes are removed and
process operates only under the Common
Causes. Process must be in statistical control
and stable
This is a measure of the ability of the process to meet the
specified tolerances.
Process Capability
When Calculate Process Capability ?
•All the Assignable Causes are removed and
process operates only under the Common
Causes. Process must be in statistical control
and stable
This is a measure of the ability of the process to meet the
specified tolerances.
-3 s +3 s
Process Width
Voice of the Process
Voice of the Customer
T
Design Width
USL LSL
Process Capability
87
Process Width
Voice of the Process
Voice of the Customer
T
Design Width
USL LSL
Process Capability
87
88
•Calculate Process Standard Deviation
s= R/d
2
d
2is a constant varying as per sample size (n)
➢Calculate Process Capability Ratio (Cp)
Cp= (USL -LSL) / 6s USL = Upper Specification Limit
= Tolerance/ 6s LSL = Lower Specification Limit
Process Capability
•Calculate Process Standard Deviation
s= R/d
2
d
2is a constant varying as per sample size (n)
➢Calculate Process Capability Ratio (Cp)
Cp= (USL -LSL) / 6s USL = Upper Specification Limit
= Tolerance/ 6s LSL = Lower Specification Limit
Process Capability
Cp represents the precision, but not the accuracy of the process in respect
to the tolerance window.
Process Capability
High Accuracy but low
precision
High Precision but low
Accuracy
to the tolerance window.
Process Capability
High Accuracy but low
precision
High Precision but low
Accuracy
Computing C
p
Calculate the Process Capability(Cp) for the following process:
Specification = 9.0 0.5
Process mean = 8.80
Process standard deviation = 0.12
90
p
Calculate the Process Capability(Cp) for the following process:
Specification = 9.0 0.5
Process mean = 8.80
Process standard deviation = 0.12
90
Specification = 9.0 0.5
Process mean = 8.80
Process standard deviation = 0.12
C
p=
= = 1.39
USL-LSL
6s
9.5 -8.5
6(0.12)
91
Computing C
p
Process mean = 8.80
Process standard deviation = 0.12
C
p=
= = 1.39
USL-LSL
6s
9.5 -8.5
6(0.12)
91
Computing C
p
Process Capability
Design
Specifications
Process
92
(a) Natural variation exceeds design specifications; process is not capable of
meeting specifications all the time.
Design
Specifications
Process
92
(a) Natural variation exceeds design specifications; process is not capable of
meeting specifications all the time.
Process Capability
Design
Specifications
Process
93
(b) Design specifications and natural variation the same; process is
capable of meeting specifications most of the time.
Design
Specifications
Process
93
(b) Design specifications and natural variation the same; process is
capable of meeting specifications most of the time.
Design Specifications
Process
94
(c) Design specifications greater than natural variation; process is capable of
always conforming to specifications.
Process Capability
Process
94
(c) Design specifications greater than natural variation; process is capable of
always conforming to specifications.
Process Capability
95
Process Capability Index ( Cpk)
Cp
U= (USL -X) / 3s
and Cp
L= (X -LSL) / 3s
Whichever is minimum will be Cpk
Process Capability Index ( Cpk)
Cp
U= (USL -X) / 3s
and Cp
L= (X -LSL) / 3s
Whichever is minimum will be Cpk
Computing C
pk
96
Calculate the Process Capability(Cpk) for the following process:
Specification = 9.0 0.5
Process mean = 8.80
Process standard deviation = 0.12
pk
96
Calculate the Process Capability(Cpk) for the following process:
Specification = 9.0 0.5
Process mean = 8.80
Process standard deviation = 0.12
Specification = 9.0 0.5
Process mean = 8.80
Process standard deviation = 0.12
C
pk= minimum
= minimum , = 0.83
x -lower specification limit
3s
=
upper specification limit -x
3s
=
,
8.80 -8.50
3(0.12)
9.50 -8.80
3(0.12)
97
Computing C
pk
Process mean = 8.80
Process standard deviation = 0.12
C
pk= minimum
= minimum , = 0.83
x -lower specification limit
3s
=
upper specification limit -x
3s
=
,
8.80 -8.50
3(0.12)
9.50 -8.80
3(0.12)
97
Computing C
pk
A Problem with Cp
✓How much is Cp
✓Which one is the better process
98
Look at these 2 processes:
✓How much is Cp
✓Which one is the better process
98
Look at these 2 processes:
➢Cpconsiders only spread, not the location
➢For a truly capable process
•Process spread must be smaller to specification and
•It should be located in a manner that its spread on both the sides falls well with in specification.
Capability index that considers both location and spread is called Cpk
99
A Problem with Cp
➢For a truly capable process
•Process spread must be smaller to specification and
•It should be located in a manner that its spread on both the sides falls well with in specification.
Capability index that considers both location and spread is called Cpk
99
A Problem with Cp
Computing Cpand Cpk
Calculate Cpand Cpkof this process
No. of data = 125
No. of subgroup = 25
Frequency of subgroup = One sub group/shift
Specification = 0.7 +/-0.2
Process Mean = 0.738
Average Range = 0.169
100Subgroup
Size (n)
A2 d2 D3 D4 E2
2 1.880 1.128 - 3.267 2.660
3 1.023 1.693 - 2.574 1.772
4 0.729 2.059 - 2.282 1.457
5 0.577 2.326 - 2.114 1.290
6 0.483 2.534 - 2.004 1.184
7 0.419 2.704 0.076 1.924 1.109
8 0.373 2.847 0.136 1.864 1.054
9 0.337 2.970 0.184 1.816 1.010
Calculate Cpand Cpkof this process
No. of data = 125
No. of subgroup = 25
Frequency of subgroup = One sub group/shift
Specification = 0.7 +/-0.2
Process Mean = 0.738
Average Range = 0.169
100Subgroup
Size (n)
A2 d2 D3 D4 E2
2 1.880 1.128 - 3.267 2.660
3 1.023 1.693 - 2.574 1.772
4 0.729 2.059 - 2.282 1.457
5 0.577 2.326 - 2.114 1.290
6 0.483 2.534 - 2.004 1.184
7 0.419 2.704 0.076 1.924 1.109
8 0.373 2.847 0.136 1.864 1.054
9 0.337 2.970 0.184 1.816 1.010
Specification = 0.7 0.2
Average range = 0.169
Process standard deviation = 0.169/2.326=0.073
C
p=
= 0.913
USL-LSL
6s
0.9 –0.5
6(0.0.073)
Computing Cpand Cpk
Average range = 0.169
Process standard deviation = 0.169/2.326=0.073
C
p=
= 0.913
USL-LSL
6s
0.9 –0.5
6(0.0.073)
Computing Cpand Cpk
Specification = 0.7 0.2
Process mean = 0.738
Process standard deviation = 0.073
C
pk= minimum
= minimum , = 0.74
x -lower specification limit
3s
=
upper specification limit -x
3s
=
,
0.738 –0.5
3(0.0.073)
0.9 –0.738
3(0.073)
102
Computing Cpand Cpk
Process mean = 0.738
Process standard deviation = 0.073
C
pk= minimum
= minimum , = 0.74
x -lower specification limit
3s
=
upper specification limit -x
3s
=
,
0.738 –0.5
3(0.0.073)
0.9 –0.738
3(0.073)
102
Computing Cpand Cpk
Machines must be capable of meeting the design specification of 15.8-16.2 gm
with observed process average 15.9 gm
•Machine A
Cp= Cpk=
•Machine B
Cp= Cpk=
•Machine C
Cp= Cpk=
Machine σ
A .05
B .1
C .2
Computing the Cp/CpkValue
103
with observed process average 15.9 gm
•Machine A
Cp= Cpk=
•Machine B
Cp= Cpk=
•Machine C
Cp= Cpk=
Machine σ
A .05
B .1
C .2
Computing the Cp/CpkValue
103
Cp Cpk Remarks
•Process capable
•Continue charting
•Bring Cpkcloser to Cp
X
•Process has potential capability
•Improve Cpkby local action
X X
•Process lacks basic capability
•Improve process by management action
Cpand Cpk
104
•Process capable
•Continue charting
•Bring Cpkcloser to Cp
X
•Process has potential capability
•Improve Cpkby local action
X X
•Process lacks basic capability
•Improve process by management action
Cpand Cpk
104
Sigma Level or Z Score
105
105
106
Sigma Level or Z score
Cp
U= (USL -X) / 3s
and Cp
L= (X -LSL) / 3s
Whichever is minimum will be Cpk
sLevel
U= (USL -X) / s
and sLevel
L= (X -LSL) / s
Whichever is minimum , that will the Sigma level of the
process
If 3 is removed from there,
Sigma Level or Z score
Cp
U= (USL -X) / 3s
and Cp
L= (X -LSL) / 3s
Whichever is minimum will be Cpk
sLevel
U= (USL -X) / s
and sLevel
L= (X -LSL) / s
Whichever is minimum , that will the Sigma level of the
process
If 3 is removed from there,
Specification = 5-15
Process mean = 9.0
Process standard deviation = 1.6
107
Sigma level
Process mean = 9.0
Process standard deviation = 1.6
107
Sigma level
Specification = 5-15
Process mean = 9.0
Process standard deviation = 1.6
sLevel= min.
= minimum , = 2.5
x -lower specification limit
s
=
upper specification limit -x
s
=
,
9-5
1.6
15-9
1.6
108
Sigma level
Process mean = 9.0
Process standard deviation = 1.6
sLevel= min.
= minimum , = 2.5
x -lower specification limit
s
=
upper specification limit -x
s
=
,
9-5
1.6
15-9
1.6
108
Sigma level
Cpkand Sigma Level
Basically Cpk= Sigma Level / 3
Or Sigma level=3 X Cpk
If Cpk=1.33, sigma level= 3 X 1.33= 4
Cpk=1.67, Sigma Level= 3 X 1.67=5
Cpk=2.0, Sigma Level= 3 X 2.0 =6
Basically Cpk= Sigma Level / 3
Or Sigma level=3 X Cpk
If Cpk=1.33, sigma level= 3 X 1.33= 4
Cpk=1.67, Sigma Level= 3 X 1.67=5
Cpk=2.0, Sigma Level= 3 X 2.0 =6
What about Process Performance
➢Process capability ( Cp, Cpk) indicates the ability of a process to meet the
specification when process operates under common causes.
➢In practical situation, a process shows variation due to both common and
special causes.
➢Analysis of process behavior due to combined effect of common & special
causes is also must. The index is known as Process Performance Index (
Pp, Ppk)
Process Performance
110
➢Process capability ( Cp, Cpk) indicates the ability of a process to meet the
specification when process operates under common causes.
➢In practical situation, a process shows variation due to both common and
special causes.
➢Analysis of process behavior due to combined effect of common & special
causes is also must. The index is known as Process Performance Index (
Pp, Ppk)
Process Performance
110
Standard Deviation
Process Performance
Pp= (USL -LSL) / 6s
s = (0.900 -0.500) / 6 x 0.0759
= 0.880
Ppk
U= (USL -X) / 3s
s = (0.900 -0.738) / 3 x 0.0759
= 0.710
Ppk
L= (X -LSL) / 3s
s = (0.738 -0.500) / 3 x 0.0759
= 1.045
Ppk = 0.710
s
s=
i=1 (x
i-X)
2 for n=80
n-1
Process Performance
Process capability –6sigma range process variation of a stable process and
sigma is estimated by R bar/d2
Process Performance–6 sigma range of total process variation and is
estimated by using all individual readings
USL = 0.900
LSL = 0.500
111
Process Performance
Pp= (USL -LSL) / 6s
s = (0.900 -0.500) / 6 x 0.0759
= 0.880
Ppk
U= (USL -X) / 3s
s = (0.900 -0.738) / 3 x 0.0759
= 0.710
Ppk
L= (X -LSL) / 3s
s = (0.738 -0.500) / 3 x 0.0759
= 1.045
Ppk = 0.710
s
s=
i=1 (x
i-X)
2 for n=80
n-1
Process Performance
Process capability –6sigma range process variation of a stable process and
sigma is estimated by R bar/d2
Process Performance–6 sigma range of total process variation and is
estimated by using all individual readings
USL = 0.900
LSL = 0.500
111
Cpk Ppk Remarks
•Process capable and performing
•Continue charting
X
•Process has capability but not performing due to
special causes
•Remove special causes by local actions
X X
•Process neither capable not performing
•May require management action
Cpkand Ppk
112
•Process capable and performing
•Continue charting
X
•Process has capability but not performing due to
special causes
•Remove special causes by local actions
X X
•Process neither capable not performing
•May require management action
Cpkand Ppk
112
Process Capability Study with
only one specification (Unilateral
Tolerances)
113
only one specification (Unilateral
Tolerances)
113
Only One Specification or Tolerance(Unilateral Tolerances)
If you have only one specification ortolerance–for example, an upper, but no
lower, tolerance? How Cp and Cpkcalculated under these circumstances?
When faced with a missing specification, consider one of the following three
options:
➢Not calculatingC
pk, since all the variables are not known
➢Entering an arbitrary specification
➢Ignoring the missing specification and calculatingC
pkon the only Z-value available
114
Process capability for Unilateral Tolerances
If you have only one specification ortolerance–for example, an upper, but no
lower, tolerance? How Cp and Cpkcalculated under these circumstances?
When faced with a missing specification, consider one of the following three
options:
➢Not calculatingC
pk, since all the variables are not known
➢Entering an arbitrary specification
➢Ignoring the missing specification and calculatingC
pkon the only Z-value available
114
Process capability for Unilateral Tolerances
Example: Moulded Parts Manufacturer
A customer of a plastic moulded parts has specified that the parts should have a low amount of
moisture content. The lower the moisture content, the better, but no more than 0.5 units is
allowed; too much moisture will create manufacturing problems for the customer. The process is
in statistical control.
Assume theX-bar= 0.0025 and estimated sigma is 0.15.
Process capability for Unilateral Tolerances
A customer of a plastic moulded parts has specified that the parts should have a low amount of
moisture content. The lower the moisture content, the better, but no more than 0.5 units is
allowed; too much moisture will create manufacturing problems for the customer. The process is
in statistical control.
Assume theX-bar= 0.0025 and estimated sigma is 0.15.
Process capability for Unilateral Tolerances
Moisture content= 0.5 max
X-bar= 0.0025 and estimated sigma is 0.15
Process capability for Unilateral Tolerances
The customer is not likely to be satisfied with aC
pkof 0.005, and that number does not
represent the process capability accurately
X-bar= 0.0025 and estimated sigma is 0.15
Process capability for Unilateral Tolerances
The customer is not likely to be satisfied with aC
pkof 0.005, and that number does not
represent the process capability accurately
Assumes that the lower specification is missing. Without an LSL,Z
loweris missing or non
existent. Z
minbecomes Z
upperandC
pkbecomesZ
upper/ 3.
Z
upper= 3.316 (from above)
C
pk= 3.316 / 3 = 1.10
AC
pkof 1.10 is more realistic than one of 0.005 for the data given in this example, and is
more representative of the process itself
Process capability for Unilateral Tolerances
loweris missing or non
existent. Z
minbecomes Z
upperandC
pkbecomesZ
upper/ 3.
Z
upper= 3.316 (from above)
C
pk= 3.316 / 3 = 1.10
AC
pkof 1.10 is more realistic than one of 0.005 for the data given in this example, and is
more representative of the process itself
Process capability for Unilateral Tolerances
Process capability for Unilateral Tolerances
118
Summary
The (only) specification you have should be used, and the other specification should be left out of
consideration or treated as missing and not be artificially inserted into the calculation
Cphas no meaning for unilateral tolerances.
Cpkis equal to CPU or CPL depending upon whether the tolerance is an USL or LSL
CPU= USL-X double Bar/ 3 sigma (R bar/d2)
CPL = X double Bar-LSL/ 3 sigma ( R bar/d2)
118
Summary
The (only) specification you have should be used, and the other specification should be left out of
consideration or treated as missing and not be artificially inserted into the calculation
Cphas no meaning for unilateral tolerances.
Cpkis equal to CPU or CPL depending upon whether the tolerance is an USL or LSL
CPU= USL-X double Bar/ 3 sigma (R bar/d2)
CPL = X double Bar-LSL/ 3 sigma ( R bar/d2)
Suggested use of process measures
It is difficult to assess or truly understand a process on the basis of a single index.
No single index should be used to describe a process. It is strongly recommended
that all four indices( Cp, Cpk, Ppand Ppkbe calculated on the same data set.)
Low Cp, Cpkvalues may indicate within subgroup variability issue, whereas low
Pp, Ppkvalues indicate overall variability issue.
119
Cp, Cpkand Pp, Ppk
It is difficult to assess or truly understand a process on the basis of a single index.
No single index should be used to describe a process. It is strongly recommended
that all four indices( Cp, Cpk, Ppand Ppkbe calculated on the same data set.)
Low Cp, Cpkvalues may indicate within subgroup variability issue, whereas low
Pp, Ppkvalues indicate overall variability issue.
119
Cp, Cpkand Pp, Ppk
Control charts-Ongoing Process Control
120
120
➢Collect the data at the frequency as established
➢Plot on control chart
➢Perform instant analysis and interpretation
➢Give immediate feed back to the process for action if any indication of change in
process behavior
➢Record significant process events ( Tool change, operator change, raw material
batch change, shift change, breakdown etc…
➢This helps in identifying the special causes
121
Ongoing Process Control
➢Plot on control chart
➢Perform instant analysis and interpretation
➢Give immediate feed back to the process for action if any indication of change in
process behavior
➢Record significant process events ( Tool change, operator change, raw material
batch change, shift change, breakdown etc…
➢This helps in identifying the special causes
121
Ongoing Process Control
122
Interpretation for Process Control Chart
Run Trend (increasing)
Trend (decreasing)
Cyclic pattern/trendTwo universe patternOut of control (no trend)
-------------------------
-------------------------
-------------------------
-------------------------
-------------------------
-------------------------
-------------------------
-------------------------
-------------------------
-------------------------
-------------------------
-------------------------
Interpretation for Process Control Chart
Run Trend (increasing)
Trend (decreasing)
Cyclic pattern/trendTwo universe patternOut of control (no trend)
-------------------------
-------------------------
-------------------------
-------------------------
-------------------------
-------------------------
-------------------------
-------------------------
-------------------------
-------------------------
-------------------------
-------------------------
Rules for Determining Special-Cause Variation in a
Control Chart
123
Control Chart
123
Summary of Typical Special Cause Criteria1 1 Point more than 3 standard deviations from centerline
2 7 Points in a row on same side of Cenerline
3 6 Points in a row, all increasing or all decreasing
4 14 Points in a row, alternating up & Down
5 2 out of 3 points > 2 standard deviations from centerline ( same side )
6 4 out of 5 points > 1 standard deviations from centerline ( same side )
7 15 points in a row within 1 standard deviation of centerline ( either side )
8 8 Points in a row > 1 Standard deviation from centerline ( either side )
124
Defining “Out of Control” signals
2 7 Points in a row on same side of Cenerline
3 6 Points in a row, all increasing or all decreasing
4 14 Points in a row, alternating up & Down
5 2 out of 3 points > 2 standard deviations from centerline ( same side )
6 4 out of 5 points > 1 standard deviations from centerline ( same side )
7 15 points in a row within 1 standard deviation of centerline ( either side )
8 8 Points in a row > 1 Standard deviation from centerline ( either side )
124
Defining “Out of Control” signals
•One point beyond the upper or lower control limit (
beyond zone A)
Test 1 ( basic test)
✓Caused by a shift in a process
✓Requires immediate action
125
beyond zone A)
Test 1 ( basic test)
✓Caused by a shift in a process
✓Requires immediate action
125
-Seven points in a row on one side of the centreline
✓Caused by process mean shift
Test -2
126
✓Caused by process mean shift
Test -2
126
-Six points in a row, all increasing or all decreasing
✓Caused by mechanical wear
✓Chemical depletion
✓Increasing contamination
Test 3 (Trends up or down )
127
✓Caused by mechanical wear
✓Chemical depletion
✓Increasing contamination
Test 3 (Trends up or down )
127
-Fourteen points in a row alternating up and down
✓Over adjustment
✓Shift to shift variation
✓Machine to machine variation
Test -4
128
✓Over adjustment
✓Shift to shift variation
✓Machine to machine variation
Test -4
128
Test 5-Two out of three points in a row in the same zone A or beyond
Test 6-Four out of five points in a row in the same Zone B or beyond
Test 5 & 6
129
Test 6-Four out of five points in a row in the same Zone B or beyond
Test 5 & 6
129
-Fifteen points in a row in Zone C( above or below the centerline)
✓Occurs when within sub group variation large compared to between
sub group variation
✓Old or incorrectly calculated limits
Test -7
130
✓Occurs when within sub group variation large compared to between
sub group variation
✓Old or incorrectly calculated limits
Test -7
130
-Eight points in a row on both sides of the centerline with none of the points in Zone C
✓Mixtures
✓Two different processes on the same chart
Test -8
131
✓Mixtures
✓Two different processes on the same chart
Test -8
131
X Bar chartR chart Conclusion
UnderControl Under controlEnjoy
Under control Out of controlSpread change
Out of control Under controlLocation change
Out of control Out of controlBoth spread & Location change
Interpretation of control chart
132
UnderControl Under controlEnjoy
Under control Out of controlSpread change
Out of control Under controlLocation change
Out of control Out of controlBoth spread & Location change
Interpretation of control chart
132
MachineCapability
133
133
Machine Capability( Cm, Cmk)
A process variation is affected by many factors like
➢Raw material variation
➢Tools
➢Operators
➢Measurement System
➢Time
➢Environment Change
Machine capability is an index which is calculated on the basis of
variation contributed by Machine only.
134
A process variation is affected by many factors like
➢Raw material variation
➢Tools
➢Operators
➢Measurement System
➢Time
➢Environment Change
Machine capability is an index which is calculated on the basis of
variation contributed by Machine only.
134
➢Take 50-100 consecutive samples/measurements in a short span.
➢Ensure the following do not change during sampling
▪Raw material batch
▪Operator
▪Measurement System
▪Tooling
▪Method of process
▪Environment etc…..
Calculate Cm, Cmkusing the same formula used for Cp, Cpk
135
Machine Capability( Cm, Cmk)
➢Ensure the following do not change during sampling
▪Raw material batch
▪Operator
▪Measurement System
▪Tooling
▪Method of process
▪Environment etc…..
Calculate Cm, Cmkusing the same formula used for Cp, Cpk
135
Machine Capability( Cm, Cmk)
Other Charts
136
136
137
X-S Charts
X-S Charts
X-S Charts
The Center Line and Control Limits of a X Chart are
The Center Line and Control Limits of a S Chart areSBLCL
SLineCenter
SBUCL
3
4
=
=
= SAXLCL
XLineCenter
SAXUCL
3
3
−=
=
+=
138
The Center Line and Control Limits of a X Chart are
The Center Line and Control Limits of a S Chart areSBLCL
SLineCenter
SBUCL
3
4
=
=
= SAXLCL
XLineCenter
SAXUCL
3
3
−=
=
+=
138
ShewhartConstantsn A2 A3 d2 c4 B3 B4 D3 D4
2 1.880 2.659 1.128 0.7979 0 3.267 0 3.267
3 1.023 1.954 1.693 0.8862 0 2.568 0 2.575
4 0.729 1.628 2.059 0.9213 0 2.266 0 2.282
5 0.577 1.427 2.326 0.9400 0 2.089 0 2.115
6 0.483 1.287 2.534 0.9515 0.030 1.970 0 2.004
7 0.419 1.182 2.704 0.9594 0.118 1.882 0.076 1.924
8 0.373 1.099 2.847 0.9650 0.185 1.815 0.136 1.864
9 0.337 1.032 2.970 0.9693 0.239 1.761 0.184 1.816
10 0.308 0.975 3.078 0.9727 0.284 1.716 0.223 1.777
11 0.285 0.927 3.173 0.9754 0.321 1.679 0.256 1.744
12 0.266 0.886 3.258 0.9776 0.354 1.646 0.283 1.717
13 0.249 0.850 3.336 0.9794 0.382 1.618 0.307 1.693
14 0.235 0.817 3.407 0.9810 0.406 1.594 0.328 1.672
15 0.223 0.789 3.472 0.9823 0.428 1.572 0.347 1.653
16 0.212 0.763 3.532 0.9835 0.448 1.552 0.363 1.637
17 0.203 0.739 3.588 0.9845 0.466 1.534 0.378 1.622
18 0.194 0.718 3.640 0.9854 0.482 1.518 0.391 1.608
19 0.187 0.698 3.689 0.9862 0.497 1.503 0.403 1.597
20 0.180 0.680 3.735 0.0969 0.510 1.490 0.415 1.585
21 0.173 0.663 3.778 0.9876 0.523 1.477 0.425 1.575
22 0.167 0.647 3.819 0.9882 0.534 1.466 0.434 1.566
23 0.162 0.633 3.858 0.9887 0.545 1.455 0.443 1.557
24 0.157 0.619 3.895 0.9892 0.555 1.445 0.451 1.548
25 0.153 0.606 3.931 0.9896 0.565 1.435 0.459 1.541
139
2 1.880 2.659 1.128 0.7979 0 3.267 0 3.267
3 1.023 1.954 1.693 0.8862 0 2.568 0 2.575
4 0.729 1.628 2.059 0.9213 0 2.266 0 2.282
5 0.577 1.427 2.326 0.9400 0 2.089 0 2.115
6 0.483 1.287 2.534 0.9515 0.030 1.970 0 2.004
7 0.419 1.182 2.704 0.9594 0.118 1.882 0.076 1.924
8 0.373 1.099 2.847 0.9650 0.185 1.815 0.136 1.864
9 0.337 1.032 2.970 0.9693 0.239 1.761 0.184 1.816
10 0.308 0.975 3.078 0.9727 0.284 1.716 0.223 1.777
11 0.285 0.927 3.173 0.9754 0.321 1.679 0.256 1.744
12 0.266 0.886 3.258 0.9776 0.354 1.646 0.283 1.717
13 0.249 0.850 3.336 0.9794 0.382 1.618 0.307 1.693
14 0.235 0.817 3.407 0.9810 0.406 1.594 0.328 1.672
15 0.223 0.789 3.472 0.9823 0.428 1.572 0.347 1.653
16 0.212 0.763 3.532 0.9835 0.448 1.552 0.363 1.637
17 0.203 0.739 3.588 0.9845 0.466 1.534 0.378 1.622
18 0.194 0.718 3.640 0.9854 0.482 1.518 0.391 1.608
19 0.187 0.698 3.689 0.9862 0.497 1.503 0.403 1.597
20 0.180 0.680 3.735 0.0969 0.510 1.490 0.415 1.585
21 0.173 0.663 3.778 0.9876 0.523 1.477 0.425 1.575
22 0.167 0.647 3.819 0.9882 0.534 1.466 0.434 1.566
23 0.162 0.633 3.858 0.9887 0.545 1.455 0.443 1.557
24 0.157 0.619 3.895 0.9892 0.555 1.445 0.451 1.548
25 0.153 0.606 3.931 0.9896 0.565 1.435 0.459 1.541
139
Moving Range( I & MR Charts)
140
140
When to use :
➢Measurement is variable
➢The measurement are expensive and/or destructive
➢Production rate is slow or
➢Population is homogeneous
The individual control charts are useful for samples of sizes n = 1.
I & MR Charts
141
➢Measurement is variable
➢The measurement are expensive and/or destructive
➢Production rate is slow or
➢Population is homogeneous
The individual control charts are useful for samples of sizes n = 1.
I & MR Charts
141
I & MR Charts
142
•The moving range(MR) is defined as the absolute difference between two
successive observations:
MR
i= |x
i-x
i-1|
which will indicate possible shifts or changes in the process from one
observation to the next.
142
•The moving range(MR) is defined as the absolute difference between two
successive observations:
MR
i= |x
i-x
i-1|
which will indicate possible shifts or changes in the process from one
observation to the next.
143
Note:TheControlChartforProcessPerformance
monitoringofslowproductionrateordestructivetesting
•UpperControlLimitsUCL
X=
•LowerControlLimitsLCL
X=
•UpperControlLimitsUCL
R=
•LowerControlLimitsLCL
R=
X-E
2R
X+E
2R
D
3R
D
4R
I & MR Charts
Note:TheControlChartforProcessPerformance
monitoringofslowproductionrateordestructivetesting
•UpperControlLimitsUCL
X=
•LowerControlLimitsLCL
X=
•UpperControlLimitsUCL
R=
•LowerControlLimitsLCL
R=
X-E
2R
X+E
2R
D
3R
D
4R
I & MR Charts
I & MR Charts
Sub group
size (n )
d2 D3 D4 E2
2 1.128 - 3.267 2.660
3 1.693 - 2.574 1.772
4 2.059 - 2.282 1.457
5 2.326 - 2.114 1.290
6 2.534 - 2.004 1.184
7 2.704 0.076 1.924 1.109
8 2.847 0.136 1.864 1.054
9 2.970 0.184 1.816 1.010
Constants table for I-MR Chart
145
I & MR Charts
size (n )
d2 D3 D4 E2
2 1.128 - 3.267 2.660
3 1.693 - 2.574 1.772
4 2.059 - 2.282 1.457
5 2.326 - 2.114 1.290
6 2.534 - 2.004 1.184
7 2.704 0.076 1.924 1.109
8 2.847 0.136 1.864 1.054
9 2.970 0.184 1.816 1.010
Constants table for I-MR Chart
145
I & MR Charts
I & MR Charts
•X Charts can be interpreted similar to charts MR charts cannot be
interpreted the same as or R charts.
•Since the MR chart plots data that are “correlated” with one another, then
looking for patterns on the chart does not make sense.
•MR chart cannot really supply useful information about process variability.
•More emphasis should be placed on interpretation of the X chart.
Interpretation of the Chartsx
147x
I & MR Charts
interpreted the same as or R charts.
•Since the MR chart plots data that are “correlated” with one another, then
looking for patterns on the chart does not make sense.
•MR chart cannot really supply useful information about process variability.
•More emphasis should be placed on interpretation of the X chart.
Interpretation of the Chartsx
147x
I & MR Charts
Stoplight Control Chart
148
148
With this chart process location and variation are controlled using one chart
Scenario will divide the process variation into three parts : warning low
(yellow zone), target(green zone) and warning high(yellow zone). Area
outside the expected process variation(6 sigma) is stop zones(red).
Assumptions in this spotlight chart are:
1.Process is in statistical control
2. Measurement variability is acceptable
3.Process performance is acceptable.
4.Process is on target
149
Stoplight control charts
Scenario will divide the process variation into three parts : warning low
(yellow zone), target(green zone) and warning high(yellow zone). Area
outside the expected process variation(6 sigma) is stop zones(red).
Assumptions in this spotlight chart are:
1.Process is in statistical control
2. Measurement variability is acceptable
3.Process performance is acceptable.
4.Process is on target
149
Stoplight control charts
TUV INDIA, Member of TÜV
NORD Group
Stop
Warning
Target
Warning
Stop
LSL
USL
+1.5 standard deviation is labeled as green, rest within the
process distribution as yellow
If the process distribution follows the normal form,
~ 86.6% of the distribution is in the green area,
~13.2% is in the yellow area
~ 0.3% is in the red area
Two-stage sampling (2,3)
➢Focus of this tool is to detect the changes(special cause of variation) in the process.
➢It requires no computation, no plotting. Hence easier to implement at operator level.
➢+1.5 standard deviation is labeled as green, rest within the process distribution as yellow.
Stoplight control charts
Stop
Warning
Target
Warning
Stop
LSL
USL
Stop
Warning
Target
Warning
Stop
LSL
USL
Stop
Warning
Target
Warning
Stop
LSL
USL
Stop
Warning
Target
Warning
Stop
LSL
USL
Stop
Warning
Target
Warning
Stop
LSL
USL
NORD Group
Stop
Warning
Target
Warning
Stop
LSL
USL
+1.5 standard deviation is labeled as green, rest within the
process distribution as yellow
If the process distribution follows the normal form,
~ 86.6% of the distribution is in the green area,
~13.2% is in the yellow area
~ 0.3% is in the red area
Two-stage sampling (2,3)
➢Focus of this tool is to detect the changes(special cause of variation) in the process.
➢It requires no computation, no plotting. Hence easier to implement at operator level.
➢+1.5 standard deviation is labeled as green, rest within the process distribution as yellow.
Stoplight control charts
Stop
Warning
Target
Warning
Stop
LSL
USL
Stop
Warning
Target
Warning
Stop
LSL
USL
Stop
Warning
Target
Warning
Stop
LSL
USL
Stop
Warning
Target
Warning
Stop
LSL
USL
Stop
Warning
Target
Warning
Stop
LSL
USL
Procedure:
1.Check 2 pcs, if both pcs are in green zone, continue to run.
2.If one or both are in red zone, stop the process. Plan for corrective action and sort the material. When
setup or other corrections are made, repeat step-1
3.If one or both are in yellow zone, check 3 more pcs. If any pc fall in red zone, stop the process. Plan for
corrective action and sort the material. When setup or other corrections are made, repeat step-1
➢If no pcs fall in red zone, but 3 or more are in yellow zone(out of 5 pcs.) stop the process. Plan for
corrective action and sort the material. When setup or other corrections are made, repeat step-1
➢If 3 pcs are in green zone and the rest are yellow, continue to run
151
Stoplight control charts
1.Check 2 pcs, if both pcs are in green zone, continue to run.
2.If one or both are in red zone, stop the process. Plan for corrective action and sort the material. When
setup or other corrections are made, repeat step-1
3.If one or both are in yellow zone, check 3 more pcs. If any pc fall in red zone, stop the process. Plan for
corrective action and sort the material. When setup or other corrections are made, repeat step-1
➢If no pcs fall in red zone, but 3 or more are in yellow zone(out of 5 pcs.) stop the process. Plan for
corrective action and sort the material. When setup or other corrections are made, repeat step-1
➢If 3 pcs are in green zone and the rest are yellow, continue to run
151
Stoplight control charts
Pre-Control Chart
152
152
Pre-control charts
TUV INDIA, Member of TÜV
NORD Group
An application of stoplight control approach for the purpose of nonconformance control. Is based on
specificationand not on process variation
It is not a process control chart but a nonconformance chart
Assumptions: special sources of variations are controlled, process performance is less than or equal to
tolerance(99.73% parts are with in specs without sorting)
Sample size: 2 (after producing 5 consecutive parts in green zone)
LSL
USL
Nom –½ Tol
Nom + ½ Tol
Nom + ¼ Tol
Nom –¼ Tol
Nominal
TUV INDIA, Member of TÜV
NORD Group
An application of stoplight control approach for the purpose of nonconformance control. Is based on
specificationand not on process variation
It is not a process control chart but a nonconformance chart
Assumptions: special sources of variations are controlled, process performance is less than or equal to
tolerance(99.73% parts are with in specs without sorting)
Sample size: 2 (after producing 5 consecutive parts in green zone)
LSL
USL
Nom –½ Tol
Nom + ½ Tol
Nom + ¼ Tol
Nom –¼ Tol
Nominal
•Pre-control sampling uses 2 parts. Before sampling, process must produce 5
consecutive parts in green zone.
•Following rules should be used
➢Two data points in green –continue to run the process
➢One each in green and yellow –continue to run
➢Two points in yellow (same zone) –adjust
➢Two points in yellow (opposite zone) –stop and investigate
➢One red –stop and investigate
•Each time the process is adjusted, before sampling, process must produce 5
consecutive parts in green zone.
•Pre-control chart is non-conformance control chart. It is not process control chart. It
should not be used when Cp, Cpkare >1
154
TUV INDIA, Member of TÜV
NORD Group
Pre-control charts
consecutive parts in green zone.
•Following rules should be used
➢Two data points in green –continue to run the process
➢One each in green and yellow –continue to run
➢Two points in yellow (same zone) –adjust
➢Two points in yellow (opposite zone) –stop and investigate
➢One red –stop and investigate
•Each time the process is adjusted, before sampling, process must produce 5
consecutive parts in green zone.
•Pre-control chart is non-conformance control chart. It is not process control chart. It
should not be used when Cp, Cpkare >1
154
TUV INDIA, Member of TÜV
NORD Group
Pre-control charts
Attribute Control Charts
155
155
Attributes charts are based upon identification and counting of defects or
defective items.
Defect: A fault which causes an item to fail to meet the specification.E.g. Dent,
scratch, crack, blow holes
Defective: A unit which fails to meet specification due to the presence of one or
more defects.
Attribute Control Charts
156
defective items.
Defect: A fault which causes an item to fail to meet the specification.E.g. Dent,
scratch, crack, blow holes
Defective: A unit which fails to meet specification due to the presence of one or
more defects.
Attribute Control Charts
156
Attribute control charts are of four types which count either no. of defects or the
no. of defective items present in a sample.
Interest in Non-conforming(defective) items
np Chart –Each item is judged to be either good or bad and the no. of defective items in a
sample is monitored. Sample size must remain constant.
p Chart-In this chart, Proportion or percentage of defectiveitems in a sample is monitored.
Sample sizemay be allowed to vary by 25%
Interest in Non-conformities(defects)
c Chart –This is used when there may be many defects in a single item. A single item is
examined and the no. of defects is recorded and monitored. Sample size must remain constant.
u chart –In this chart, sample of several items is checked and the average no. of defects per
unit is recorded and monitored. Sample size may vary by as much as 25%.
157
Attribute Control Charts
no. of defective items present in a sample.
Interest in Non-conforming(defective) items
np Chart –Each item is judged to be either good or bad and the no. of defective items in a
sample is monitored. Sample size must remain constant.
p Chart-In this chart, Proportion or percentage of defectiveitems in a sample is monitored.
Sample sizemay be allowed to vary by 25%
Interest in Non-conformities(defects)
c Chart –This is used when there may be many defects in a single item. A single item is
examined and the no. of defects is recorded and monitored. Sample size must remain constant.
u chart –In this chart, sample of several items is checked and the average no. of defects per
unit is recorded and monitored. Sample size may vary by as much as 25%.
157
Attribute Control Charts
Calculation of Control Limits for Attribute Charts
•The control limits which we use in these charts are performance based limits
because we follow these steps in each type of charts:
•Collect data from the process by counting either no. of defects or defective items
in a sample
•Calculate from that data an average performance called process average
•Use that process average to derive control limits with which to monitor future
performance.
•The control limits which we use in these charts are performance based limits
because we follow these steps in each type of charts:
•Collect data from the process by counting either no. of defects or defective items
in a sample
•Calculate from that data an average performance called process average
•Use that process average to derive control limits with which to monitor future
performance.
Interpretation of Attribute Control Charts
1 Any point outside the control limits
2 Run of 7 consecutive points all above or all below the process average
(centreline)
3 Run of 7 consecutive points all going up or all going down
4 Any other non random pattern
Attribute control charts are performance based charts since the control limits used are
based on process average. If process is operating in statistical control, we would expect
all the variation to be random around the process average and contained with in the
control limits due to variation inherent in the process.
Any deviation from this random pattern would be due to some specific cause and will be
indicated by:
159
1 Any point outside the control limits
2 Run of 7 consecutive points all above or all below the process average
(centreline)
3 Run of 7 consecutive points all going up or all going down
4 Any other non random pattern
Attribute control charts are performance based charts since the control limits used are
based on process average. If process is operating in statistical control, we would expect
all the variation to be random around the process average and contained with in the
control limits due to variation inherent in the process.
Any deviation from this random pattern would be due to some specific cause and will be
indicated by:
159
Interpretation of Attribute Control Charts
1. Any of these indicates that a change has occurred either for betteror worse.
2.A point outside the upper control limit is firm evidence that the process has become
significantly worse
3. A point below the lower control limit(where applicable) shows the process has improved .
Investigative action must be taken to determine the cause of the change and
(i) remove the cause of process has deteriorated or
(ii) if the process average has improved, the attempt to build the special cause into the
process as permanent feature.
160
1. Any of these indicates that a change has occurred either for betteror worse.
2.A point outside the upper control limit is firm evidence that the process has become
significantly worse
3. A point below the lower control limit(where applicable) shows the process has improved .
Investigative action must be taken to determine the cause of the change and
(i) remove the cause of process has deteriorated or
(ii) if the process average has improved, the attempt to build the special cause into the
process as permanent feature.
160
P-Chart
UCL = p+ 3
LCL = p–3
p(1 -p)
n
p(1 -p)
n
where
p=the sample proportion defective; an estimate of the process average
161
UCL = p+ 3
LCL = p–3
p(1 -p)
n
p(1 -p)
n
where
p=the sample proportion defective; an estimate of the process average
161
20 samples of 100 prescriptions
NUMBER PROPORTION
SAMPLE DEFECTIVE DEFECTIVE
1 6 .06
2 0 .00
3 4 .04
: : :
: : :
20 18 .18
200
162
P-Chart
NUMBER PROPORTION
SAMPLE DEFECTIVE DEFECTIVE
1 6 .06
2 0 .00
3 4 .04
: : :
: : :
20 18 .18
200
162
P-Chart
NUMBER PROPORTION
SAMPLE DEFECTIVE DEFECTIVE
1 6 .06
2 0 .00
3 4 .04
: : :
: : :
20 18 .18
200
p=
= 200 / 20(100)
= 0.10
total defectives
total sample observations
163
P-Chart
SAMPLE DEFECTIVE DEFECTIVE
1 6 .06
2 0 .00
3 4 .04
: : :
: : :
20 18 .18
200
p=
= 200 / 20(100)
= 0.10
total defectives
total sample observations
163
P-Chart
p= 0.10
UCL = p+ 3 = 0.10 + 3
p(1 -p)
n
0.10(1 -0.10)
100
UCL = 0.19
LCL = 0.01
LCL = p-3 = 0.10 -3
p(1 -p)
n
0.10(1 -0.10)
100
164
P-Chart
UCL = p+ 3 = 0.10 + 3
p(1 -p)
n
0.10(1 -0.10)
100
UCL = 0.19
LCL = 0.01
LCL = p-3 = 0.10 -3
p(1 -p)
n
0.10(1 -0.10)
100
164
P-Chart
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
Proportion defective
Sample number
2 4 6 8 10 12 14 16 18 20
UCL = 0.19
LCL = 0.01
p= 0.10
165
P-Chart
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
Proportion defective
Sample number
2 4 6 8 10 12 14 16 18 20
UCL = 0.19
LCL = 0.01
p= 0.10
165
P-Chart
C Chart
U Chart
C chart and U Chart
C chart and U Chart
The number of defects in 15 sample rooms in a hotel
1 12
2 8
3 16
: :
: :
15 15
190
SAMPLE NUMBER OF DEFECTS
c= = 12.67
190
15
UCL= 12.67 + 3 12.67
= 23.35
LCL= 12.67 -3 12.67
= 1.99
170
C chart
1 12
2 8
3 16
: :
: :
15 15
190
SAMPLE NUMBER OF DEFECTS
c= = 12.67
190
15
UCL= 12.67 + 3 12.67
= 23.35
LCL= 12.67 -3 12.67
= 1.99
170
C chart
3
6
9
12
15
18
21
24
Number of defects
Sample number
2 4 6 8 10 12 14 16
UCL = 23.35
LCL = 1.99
c= 12.67
171
C chart
6
9
12
15
18
21
24
Number of defects
Sample number
2 4 6 8 10 12 14 16
UCL = 23.35
LCL = 1.99
c= 12.67
171
C chart
Where to Use SPC Charts
•When a mistake-proofing device is not feasible
•Identify processes with high RPNs from FMEA
➢Evaluate the “Current Controls” column to determine “gaps” in the control
plan. Does SPC make sense?
•Identify critical variables based on DOE
•Customer requirements
•Management commitments
172
•When a mistake-proofing device is not feasible
•Identify processes with high RPNs from FMEA
➢Evaluate the “Current Controls” column to determine “gaps” in the control
plan. Does SPC make sense?
•Identify critical variables based on DOE
•Customer requirements
•Management commitments
172
Updating Control Limits
Control Limits should be updated when:
➢Change in supplier for a critical material
➢Change in process machinery
➢Engineering change orders that affect process flow
➢Introduction of new operators
➢Change in sample size
173
Control Limits should be updated when:
➢Change in supplier for a critical material
➢Change in process machinery
➢Engineering change orders that affect process flow
➢Introduction of new operators
➢Change in sample size
173
Now your questions
are welcomed
are welcomed
Thanks for Your Participation
Rajendra Tandon
Contact No.:
9810880050
Email:
[email protected], [email protected]
175
Rajendra Tandon
Contact No.:
9810880050
Email:
[email protected], [email protected]
175
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