Statistical process control and quality management (2).ppt

Different types of of statistical techniques and quality management methods.

1. ©The McGraw-Hill Companies, Inc. 2008McGraw-Hill/Irwin
Statistical Process Control and
Quality Management
Chapter 19

2. 2
GOALS
Discuss the role of quality control in production and service
operations.
Define and understand the terms chance cause, assignable
cause, in control, out of control, attribute, and variable.
Construct and interpret a Pareto chart.
Construct and interpret a fishbone diagram.
Construct and interpret mean and range charts.
Construct and interpret percent defective and a c-bar charts.
Discuss acceptance sampling.
Construct an operating characteristic curve for various
sampling plans.

3. 3
Control Charts
Statistical Quality Control emphasizes in-process
control with the objective of controlling the quality of a
manufacturing process or service operation using
sampling techniques.
Statistical sampling techniques are used to aid in the
manufacturing of a product to specifications rather
than attempt to inspect quality into the product after it
is manufactured.
Control Charts are useful for monitoring a process.

4. 4
Causes of Variation
There is variation in all parts produced by a manufacturing
process. There are two sources of variation:
Chance Variation is random in nature and cannot be entirely eliminated.
Assignable Variation is nonrandom in nature and can be reduced or
eliminated.

5. 5
Diagnostic Charts
There are a variety of
diagnostic techniques
available to investigate
quality problems. Two of
the more prominent of
these techniques are
Pareto charts and
fishbone diagrams.

6. 6
Pareto Charts
Pareto analysis is a technique for tallying the number
and type of defects that happen within a product or
service.
The chart is named after a nineteenth-century Italian
scientist, Vilfredo Pareto. He noted that most of the
“activity” in a process is caused by relatively few of
the “factors.”
Pareto’s concept, often called the 80–20 rule, is that 80
percent of the activity is caused by 20 percent of the
factors. By concentrating on 20 percent of the factors,
managers can attack 80 percent of the problem.

7. 7
Pareto Chart - Example
The city manager of Grove
City, Utah, is concerned with
water usage, particularly in
single family homes. She
would like to develop a plan
to reduce the water usage in
Grove City. To investigate,
she selects a sample of 100
homes and determines the
typical daily water usage for
various purposes. These
sample results are as
follows.

8. 8
Pareto Chart - Minitab

9. 9
Fishbone Diagrams
Another diagnostic chart is a cause-
and-effect diagram or a fishbone
diagram. It is called a cause-and-
effect diagram to emphasize the
relationship between an effect and
a set of possible causes that
produce the particular effect.
This diagram is useful to help organize
ideas and to identify relationships.
It is a tool that encourages open
brainstorming for ideas. By
identifying these relationships we
can determine factors that are the
cause of variability in our process.
The name fishbone comes from the
manner in which the various
causes and effects are organized
on the diagram. The effect is
usually a particular problem, or
perhaps a goal, and it is shown on
the right-hand side of the diagram.
The major causes are listed on the
left-hand side of the diagram.

10. 10
Purpose of Quality Control Charts
The purpose of quality-control charts is to
portray graphically when an assignable
cause enters the production system so that it
can be identified and corrected.
This is accomplished by periodically
selecting a random sample from the current
production.

11. 11
Mean Chart for Variables
The mean or the x-bar chart is designed to control
variables such as weight, length, etc. The upper
control limit (UCL) and the lower control limit (LCL)
are obtained from the equation:
where is the mean of the sample means and is
the mean of the sample ranges
RAXLCLandRAXUCL
22 
X R

12. 12
Statistical Software, Inc., offers a toll-free number
where customers can call with problems
involving the use of their products from 7 A.M.
until 11 P.M. daily. It is impossible to have
every call answered immediately by a technical
representative, but it is important customers do
not wait too long for a person to come on the
line. Customers become upset when they hear
the message “Your call is important to us. The
next available representative will be with you
shortly” too many times. To understand its
process, Statistical Software decides to develop
a control chart describing the total time from
when a call is received until the representative
answers the call and resolves the issue raised
by the caller. Yesterday, for the 16 hours of
operation, five calls were sampled each hour.
This information is on the table, in minutes, until
the issue was resolved.
Based on this information, develop a control chart for
the mean duration of the call. Does there
appear to be a trend in the calling times? Is
there any period in which it appears that
customers wait longer than others?
Mean Chart for Variables - Example

13. 13
Appendix B.8 (portion)

14. 14
Constructing a Mean Chart
413.9
16
60.150
X
375.6
16
102
R

15. 15
13.091
)375.6)(577(.413.9

2


 andRAXUCL
5.735
)375.6)(577(.413.9
2


 RAXLCL
Mean Chart for Variables - Example

16. 16
Range Charts for Variables
A range chart shows the variation in the sample
ranges.

17. 17
Range Chart - Example
The length of time customers of
Statistical Software, Inc.,
waited from the time their
call was answered until a
technical representative
answered their question or
solved their problem is
recorded in Table 19–1.
Develop a control chart for the
range. Does it appear that
there is any time when there
is too much variation in the
operation?

18. 18
375.6
16
102
R
Range Chart - Example

19. 19
Range Chart - Example
13.483
)375.6(115.2

4


RDUCL
0
)375.6(0
3


RDLCL

20. 20
Mean and Range Charts - Minitab

21. 21
In-Control Situation

22. 22
Mean In-control, Range Out-of-control

23. 23
Mean Out-of-control, Range In-control

24. 24
Attribute Control Chart: The p-Chart
The percent defective chart is also called a
p-chart or the p-bar chart. It graphically
shows the proportion of the production that
is not acceptable. The proportion of
defectives is found by:
samples ofNumber
Defectives ofNumber Total
p

25. 25
Attribute Control Chart – The p-Chart
The UCL and LCL are computed as the mean
percent defective plus or minus 3 times the
standard error of the percents:
n
pp
pLCLandUCL
)1(
3



26. 26
p-Chart Example
Jersey Glass Company, Inc., produces
small hand mirrors. Jersey Glass
runs a day and evening shift each
weekday. Each day, the quality
assurance department (QA)
monitors the quality of the mirrors
twice during the day shift and twice
during the evening shift. After each
four-hour period, QA selects and
carefully inspects a random sample
of 50 mirrors. Each mirror is
classified as either acceptable or
unacceptable. Finally QA counts
the number of mirrors in the sample
that do not conform to quality
specifications. List below is the
result of these checks over the last
10 business days.
Construct a percent defective chart for
this process. What are the upper
and lower control limits? Interpret
the results. Does it appear the
process is out of control during the
period?

27. 27
Computing the Control Limits

28. 28
p-Chart using Minitab

29. 29
The c-chart or the c-bar chart is designed
to control the number of defects per
unit. The UCL and LCL are found by:
UCLandLCLc c 3
Attribute Control Chart : The c-Chart

30. 30
The publisher of the Oak Harbor Daily Telegraph is concerned about the
number of misspelled words in the daily newspaper. It does not print a
paper on Saturday or Sunday. In an effort to control the problem and
promote the need for correct spelling, a control chart will be used. The
number of misspelled words found in the final edition of the paper for the
last 10 days is: 5, 6, 3, 0, 4, 5, 1, 2, 7, and 4.
Determine the appropriate control limits and interpret the chart. Were there
any days during the period that the number of misspelled words was out
of control?
0 07.277.57.3
47.977.57.3
7.337.3
7.3
10
37




LCL
UCL
LCLandUCL
c
c-Chart Example

31. 31
c-Chart in Minitab

32. 32
Acceptance Sampling
Acceptance sampling is a method of
determining whether an incoming lot of
a product meets specified standards.
–It is based on random sampling
techniques.
–A random sample of n units is
obtained from the entire lot.
–c is the maximum number of
defective units that may be found in
the sample for the lot to still be
considered acceptable.

33. 33
Acceptance Sampling Procedure
Accept shipment or reject shipment? The usual procedure is to
screen the quality of incoming parts by using a statistical
sampling plan.
According to this plan, a sample of n units is randomly selected
from the lots of N units (the population). This is called
acceptance sampling. The inspection will determine the
number of defects in the sample. This number is compared with
a predetermined number called the critical number or the
acceptance number. The acceptance number is usually
designated c.
–If the number of defects in the sample of size n is less than or
equal to c, the lot is accepted.
–If the number of defects exceeds c, the lot is rejected and returned
to the supplier, or perhaps submitted to 100 percent inspection.

34. 34
Consumer’s Risk vs. Producer’s Risk in
Acceptance Sampling
Type I Error
Type II Error

35. 35
Operating Characteristic Curve
An OC curve, or operating
characteristic curve, is developed
using the binomial probability
distribution in order to determine
the probabilities of accepting lots of
various quality level.

36. 36
OC Curve - Computation Example
Sims Software purchases DVDs from DVD
International. The DVDs are packaged in
lots of 1,000 each. Todd Sims, president
of Sims Software, has agreed to accept
lots with 10 percent or fewer defective
DVDs. Todd has directed his inspection
department to select a random sample of
20 DVDs and examine them carefully. He
will accept the lot if it has two or fewer
defectives in the sample. Develop an OC
curve for this inspection plan. What is the
probability of accepting a lot that is 10
percent defective?

37. 37
OC Curve - Computation Example
This type of sampling is called attribute sampling
because the sampled item, a DVD in this case, is
classified as acceptable or unacceptable.
Let  represent the actual proportion defective in the
population.
The lot is good if  ≤ .10.
The lot is bad if  > .10.
Let X be the number of defects in the sample. The
decision rule is:
Accept the lot if X ≤ 2.
Reject the lot if X ≥ 3.

38. 38
OC Curve - Computation Example
The binomial distribution is used to compute the various values on
the OC curve. Recall that the binomial has four requirements:
1. There are only two possible outcomes. Here the DVD is either
acceptable or unacceptable.
2. There is a fixed number of trials. In this instance the number of
trials is the sample size of 20.
3. There is a constant probability of success. A success is finding
a defective DVD. The probability of success is assumed to
be .10.
4. The trials are independent. The probability of obtaining a
defective DVD on the third one selected is not related to the
likelihood of finding a defect on the fourth DVD selected.

39. 39
OC Curve - Computation Example

40. 40
OC Curve - Computation Example
To begin we determine the probability of accepting a lot that is 5 percent defective.
This means that = .05, c = 2, and n = 20. From the Excel output, the likelihood
of selecting a sample of 20 items from a shipment that contained 5 percent
defective and finding exactly 0 defects is .358. The likelihood of finding exactly
1 defect is .377, and finding 2 is .189. Hence the likelihood of 2 or fewer defects
is .924, found by .358 +.377 + .189. This result is usually written in shorthand
notation
P(x≤ 2 |  = .05 and n = 20) = .358 + .377 + .189 = .924
The likelihood of accepting a lot that is actually 10 percent defective is .677.
P(x≤ 2 |  = .10 and n = 20) = .122 + .270 + .285 = .677
The complete OC curve in the next slide (Chart 19–8) shows the smoothed curve
for all values of between 0 and about 30 percent.

41. 41
OC Curve - Computation Example

42. 42
End of Chapter 19