2. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

3. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

4. Copyright (c) 2005 John Wiley & Sons, Inc.
Process Capability
Natural tolerance limits are defined as follows:
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

5. Copyright (c) 2005 John Wiley & Sons, Inc.
Uses of process capability data:
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

6. Reasons for Poor Process Capability
Process may have good potential capability
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

7. Copyright (c) 2005 John Wiley & Sons, Inc.
Data collection steps:
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

8. Example 7-1, Glass Container Data
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

9. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

10. Probability Plotting
Mean and standard deviation could be estimated from the plot
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

11. Copyright (c) 2005 John Wiley & Sons, Inc.
The distribution may not be normal; other types of probability plots can be useful in determining the appropriate distribution. See Chapter 2, also Figure 7-6.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

12. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

13. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

14. Copyright (c) 2005 John Wiley & Sons, Inc.
Practical interpretation – relationship of PCR to the proportion of the tolerance interval used by the process:
For the hard bake process:
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

15. Copyright (c) 2005 John Wiley & Sons, Inc.
One-Sided PCR
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

16. Interpretation of the PCR
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

17. Assumptions for Interpretation of Numbers in Table 7-2
Violation of these assumptions can lead to big trouble in using the data in Table 7-2.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

18. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

19. Copyright (c) 2005 John Wiley & Sons, Inc.
Cp does not take process centering into account
It is a measure of potential capability, not actual capability
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

20. A Measure of Actual Capability
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

21. Normality and Process Capability Ratios
The assumption of normality is critical to the usual interpretation of these ratios (such as Table 7-2)
For non-normal data, options are
Transform non-normal data to normal
Extend the usual definitions of PCRs to handle non-normal data
Modify the definitions of PCRs for general families of distributions
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

22. Other Types of Process Capability Ratios (Section 7-3.5)
First generation
Second generation
Third generation
Lots of research has been done to develop ratios that overcome some of the problems with the basic ones
Not much evidence that these ratios are used to any significant extent in practice
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

23. Copyright (c) 2005 John Wiley & Sons, Inc.
Confidence intervals are an important way to express the information in a PCR
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

24. CI is wide because the sample size is small
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

25. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

26. CI is wide because the sample size is small
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

27. Copyright (c) 2005 John Wiley & Sons, Inc.
Recommended for use when the process is not in control.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

28. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

29. Copyright (c) 2005 John Wiley & Sons, Inc.
Specifications not needed to estimate parameters and establish stability
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

30. Copyright (c) 2005 John Wiley & Sons, Inc.
Since LSL = 200
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

31. Copyright (c) 2005 John Wiley & Sons, Inc.
Use DOX to isolate sources of variability
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

32. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

33. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

34. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

35. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

36. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

37. Estimating the Variance Components
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

38. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

39. The gauge is not capable by this criterion
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

40. Copyright (c) 2005 John Wiley & Sons, Inc.
Discrimination Ratio
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

41. We have focused only on precision
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

42. Copyright (c) 2005 John Wiley & Sons, Inc.
Gauge R&R Studies
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

43. Copyright (c) 2005 John Wiley & Sons, Inc.
Gauge R&R studies are usually conducted with a factorial experiment
Variance Components
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

44. Copyright (c) 2005 John Wiley & Sons, Inc.
This is a two-factor factorial experiment
ANOVA methods are used to conduct the R&R analysis
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

45. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

46. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

47. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

48. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

49. Copyright (c) 2005 John Wiley & Sons, Inc.
Negative estimates of a variance component would lead to filling a reduced model, such as, for example:
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

50. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

51. Copyright (c) 2005 John Wiley & Sons, Inc.
For this Example
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

52. Other Topics in Gauge R&R Studies
Section provides a description of methods to obtain confidence intervals on the variance components and measures of gauge R&R
Section presents a new measure of gauge capability, the probabilities of misclassification of parts
Rejecting good units (producer’s risk)
Passing bad units (consumer’s risk)
Methods for calculating these two probabilities are given
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

53. Copyright (c) 2005 John Wiley & Sons, Inc.
Linear Combinations
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

54. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

55. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

56. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

57. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

58. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

59. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

60. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

61. Copyright (c) 2005 John Wiley & Sons, Inc.
For the normal distribution with unknown mean and variance:
Difference between tolerance limits and confidence limits
Nonparametric tolerance limits can also be calculated
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

62. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

63. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.

64. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005  John Wiley & Sons, Inc.