1. Process Capability and SPC
Chapter 9A

2. OBJECTIVES Explain what statistical quality control is.
Calculate the capability of a process.
Understand how processes are monitored with control charts. 2

3. Types of Situations where SPC can be Applied
How many paint defects are there in the finish of a car?
How long does it take to execute market orders?
How well are we able to maintain the dimensional tolerance on our ball bearing assembly?
How long do customers wait to be served from our drive-through window?
LO 1

4. 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

5. Testing examples

6. Taguchi’s View of Variation
Traditional view is that quality within the range is good and that the cost of quality outside this range is constant
Taguchi views costs as increasing as variability increases, so seek to achieve zero defects and that will truly minimize quality costs
LO 1

7. Process Capability
Taguchi argues that tolerance is not a yes/no decision, but a continuous function
Other experts argue that the process should be so good the probability of generating a defect should be very low
LO 2

8. 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

9. 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

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

11. 9A-11
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

12. Process Control with Attribute Measurement: Using ρ Charts
Created for good/bad attributes
Use simple statistics to create the control limits
LO 3

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

14. 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

15. 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

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

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

18. How to Construct x and R Charts
LO 3

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

20. 9A-20
Example of x-bar and R charts: Step 1. Calculate sample means, sample ranges, mean of means, and mean of ranges. 24

21. 9A-21
Example of x-bar and R charts: Step 2. Determine Control Limit Formulas and Necessary Tabled Values 25

22. 9A-22
Example of x-bar and R charts: Steps 3&4. Calculate x-bar Chart and Plot Values
Then plot both graphs: Means to the Mean chart and Ranges to the Range chart. 26

23. 9A-23
Any Questions?