1. Process Capability and SPC
Chapter 9A
Process Capability and SPC

2. OBJECTIVES Process Variation Process Capability
Process Control Procedures
Variable data
Attribute data 2

3. Basic Forms of Variation
Assignable variation is caused by factors that can be clearly identified and possibly managed
Example: A poorly trained employee that creates variation in finished product output.
Common variation is inherent in the production process
Example: A molding process that always leaves “burrs” or flaws on a molded item. 3

4. Taguchi’s View of Variation
Traditional view is that quality within the LS and US is good and that the cost of quality outside this range is constant, where Taguchi views costs as increasing as variability increases, so seek to achieve zero defects and that will truly minimize quality costs.
Incremental
Cost of
Variability
High
Zero
Lower
Spec
Target
Upper
Traditional View
Incremental
Cost of
Variability
High
Zero
Lower
Spec
Target
Upper
Taguchi’s View 30

5. How do the limits relate to one another?
Process Capability
Process limits
Specification limits
How do the limits relate to one another? 28

6. Process Capability Index, Cpk
Capability Index shows how well parts being produced fit into design limit specifications.
As a production process produces items small shifts in equipment or systems can cause differences in production performance from differing samples.
Shifts in Process Mean 29

7. Process Capability – A Standard Measure of How Good a Process Is.
A simple ratio:
Specification Width
_________________________________________________________
Actual “Process Width”
Generally, the bigger the better.

8. This is a “one-sided” Capability Index
Process Capability
This is a “one-sided” Capability Index
Concentration on the side which is closest to the specification - closest to being “bad”

9. Upper Tolerance Limit = 16 + .05(16) = 16.8 ounces
The Cereal Box Example
We are the maker of this cereal. Consumer reports has just published an article that shows that we frequently have less than 16 ounces of cereal in a box.
Let’s assume that the government says that we must be within ± 5 percent of the weight advertised on the box.
Upper Tolerance Limit = (16) = 16.8 ounces
Lower Tolerance Limit = 16 – .05(16) = 15.2 ounces
We go out and buy 1,000 boxes of cereal and find that they weight an average of ounces with a standard deviation of .529 ounces.

10. Cereal Box Process Capability
Specification or Tolerance Limits
Upper Spec = 16.8 oz
Lower Spec = 15.2 oz
Observed Weight
Mean = oz
Std Dev = .529 oz

11. 9A-11
What does a Cpk of mean?
An index that shows how well the units being produced fit within the specification limits.
This is a process that will produce a relatively high number of defects.
Many companies look for a Cpk of 1.3 or better… 6-Sigma company wants 2.0!

12. Types of Statistical Sampling
Attribute (Go or no-go information)
Defectives refers to the acceptability of product across a range of characteristics.
Defects refers to the number of defects per unit which may be higher than the number of defectives.
p-chart application
Variable (Continuous)
Usually measured by the mean and the standard deviation.
X-bar and R chart applications 6

13. Statistical Process Control (SPC) Charts Normal Behavior
UCL
Normal Behavior
LCL
Samples over time
UCL
Possible problem, investigate
LCL
Samples over time
UCL
Possible problem, investigate
LCL
Samples over time 16

14. Control Limits are based on the Normal Curvex m z -3 -2 -1 1 2 3
Standard deviation units or “z” units. 14

15. 9A-15
Control Limits
We establish the Upper Control Limits (UCL) and the Lower Control Limits (LCL) with plus or minus 3 standard deviations from some x-bar or mean value. Based on this we can expect 99.7% of our sample observations to fall within these limits. x
99.7%
LCL
UCL 15

16. Example of Constructing a p-Chart: Required Data
Number of defects found in each sample
Sample
No.
No. of
Samples 17

17. Statistical Process Control Formulas: Attribute Measurements (p-Chart)
Given:
Compute control limits: 18

18. Example of Constructing a p-chart: Step 1
1. Calculate the sample proportions, p (these are what can be plotted on the p-chart) for each sample 19

19. Example of Constructing a p-chart: Steps 2&3
2. Calculate the average of the sample proportions
3. Calculate the standard deviation of the sample proportion 20

20. Example of Constructing a p-chart: Step 4
4. Calculate the control limits
UCL =
LCL = (or 0) 21

21. Example of Constructing a p-Chart: Step 5
5. Plot the individual sample proportions, the average
of the proportions, and the control limits
UCL
LCL

22. Example of x-bar and R Charts: Required Data23

23. 9A-23
Example of x-bar and R charts: Step 1. Calculate sample means, sample ranges, mean of means, and mean of ranges. 24

24. 9A-24
Example of x-bar and R charts: Step 2. Determine Control Limit Formulas and Necessary Tabled Values
From Exhibit 9A.6 25

26. 9A-26
Example of x-bar and R charts: Steps 3&4. Calculate x-bar Chart and Plot Values
UCL
LCL 26

27. 9A-27
Example of x-bar and R charts: Steps 5&6. Calculate R-chart and Plot Values
UCL
LCL 27

29. Answer: a. Capability index
Question Bowl
A methodology that is used to show how well parts being produced fit into a range specified by design limits is which of the following?
Capability index
Producer’s risk
Consumer’s risk
AQL
None of the above
Answer: a. Capability index 7

30. Can not be computed on data above
Question Bowl
You want to prepare a p chart and you observe 200 samples with 10 in each, and find 5 defective units. What is the resulting “fraction defective”? 25
2.5
0.0025
Can not be computed on data above
Answer: c (5/(2000x10)=0.0025) 7

31. 9A-31
Question Bowl
You want to prepare an x-bar chart. If the number of observations in a “subgroup” is 10, what is the appropriate “factor” used in the computation of the UCL and LCL?
1.88
0.31
0.22
1.78
None of the above
Answer: b. 0.31 7

32. 9A-32
Question Bowl
You want to prepare an R chart. If the number of observations in a “subgroup” is 5, what is the appropriate “factor” used in the computation of the LCL?
0.88
1.88
2.11
None of the above
Answer: a. 0 7

33. 9A-33
Question Bowl
You want to prepare an R chart. If the number of observations in a “subgroup” is 3, what is the appropriate “factor” used in the computation of the UCL?
0.87
1.00
1.88
2.11
None of the above
Answer: e. None of the above 7

34. 9A-34
End of Chapter 9A