1. CHAPTER 8TN Process Capability and Statistical Quality Control
Process Variation
Process Capability
Process Control Procedures
Acceptance Sampling 2

2. Types of Statistical Quality Control

3. Basic Forms of Variation
Assignable variation
Common variation 3

4. Taguchi’s View of Variation
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. Process Capability Process limits Tolerance 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. 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.
Variable (Continuous)
Usually measured by the mean and the standard deviation. 6

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

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

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

11. STANDARD DEVIATION TABLE
% Data Points # of Std Dev From Mean 68 95
95.5 99
99.7

12. Example of Constructing a p-Chart: Required Data17

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

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. 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
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Observation p 22

18. R Chart Type of variables control chart Shows sample ranges over time
Interval or ratio scaled numerical data
Shows sample ranges over time
Difference between smallest & largest values in inspection sample
Monitors variability in process
Example: Weigh samples of coffee & compute ranges of samples; Plot

19. R Chart Control Limits
From Table
Sample Range at Time i
# Samples

20. R Chart Example
You’re manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on 5 deliveries per day. Is the process in control?

21. R Chart Hotel Data Sample Day Delivery Time Mean Range

22. R Chart Hotel Data Sample Day Delivery Time Mean Range
Largest
Smallest
Sample Range =

23. R Chart Hotel Data Sample Day Delivery Time Mean Range
Sample Mean =

24. R Chart Hotel Data Sample Day Delivery Time Mean Range

25. Example of R charts: 25

26. Example of R charts:
From Exhibit TN7.7 25

27. R Chart Control Chart Solution
UCL

28. `X Chart Type of variables control chart Shows sample means over time
Monitors process average
Example:

29. `X Chart Control Limits
From Exhibit 7.7TN(n = 5)
Sample Mean at Time i
Sample Range at Time i
# Samples

30. `X Chart Example
You’re manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on 5 deliveries per day. Is the process in control?
Alone
Group
Class

31. X Chart Hotel Data Sample Day Delivery Time Mean Range

32. Example of x-bar charts: Tabled Values
From Exhibit TN7.7 25

33. Example of x-bar charts: Tabled Values
From Exhibit TN7.7 25

34. `X Chart Control Chart Solution*
UCL
LCL

35. Process Capability

36. Process Capability Process Capability -
TQM’s emphasis on “making it right the first time” has resulted in organizations emphasizing the ability of a production system to meet design specifications rather than evaluating the quality of outputs after the fact with acceptance sampling.
Process Capability -

37. Process Capability
Process limits –
Tolerance limits -

38. Process Capability How do the limits relate to one another?
You want: tolerance range > process range
1. Make bigger
2. Make smaller
Two methods of accomplishing this:

39. Process Capability Measurement
Cp index = Tolerance range / Process range
What value(s) would you like for Cp?
Larger Cp –
The Cp index
Assumes

40. Process Capability Depends On:
Location of the process mean.
Natural variability inherent in the process.
Stability of the process.
Product’s design requirements.

41. Natural Variation Versus Product Design Specifications

42. Process Capability Index
Cp < 1:
Cp > 1:
As rule of thumb, many organizations desire a Cp index of at least 1.5.
Six sigma quality (fewer than 3.4 defective parts per million) corresponds to a Cp index of 2.

44. LTL
UTL

45. Process Capability Light-bulb Production UTL - LTL 6s CP =
Upper specification = 120 hours
Lower specification = 80 hours
Average life = 90 hours s = 4.8 hours
UTL - LTL 6s
This slide presents the equation for the Process Capability Ratio, Cp.
CP =
Process Capability Ratio 25

46. Process Capability CP = Light-bulb Production Process Capability Ratio
This slide substitutes in the values for the specification limits and the process standard deviation.
Process Capability Ratio 26

47. Cpk Index = estimate of the process mean
s = estimate of the standard deviation
Together, these process capability Indices show how well parts being produced conform to design specifications.

48. Light-bulb Production

49. Another example of the use of process capability indices
The design specifications for a machined slot is 0.5± .003 inches. Samples have been taken and the process mean is estimated to be The process standard deviation is estimated to be .001.
What can you say about the capability of this process to produce this dimension?

50. Basic Forms of Statistical Sampling for Quality Control
Sampling to accept or reject the immediate lot of product at hand (Acceptance Sampling).
Sampling to determine if the process is within acceptable limits (Statistical Process Control)

51. Acceptance Sampling Purposes Advantages Determine quality level
Ensure quality is within predetermined level
Advantages
Economy
Less handling damage
Fewer inspectors
Upgrading of the inspection job
Applicability to destructive testing
Entire lot rejection (motivation for improvement) 4

52. Acceptance Sampling Disadvantages
Risks of accepting “bad” lots and rejecting “good” lots
Added planning and documentation
Sample provides less information than 100-percent inspection 5

53. Risk Acceptable Quality Level (AQL)
Lot Tolerance Percent Defective (LTPD) 8