1. Chapter 81Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

2. Chapter 82Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Learning Objectives

3. Chapter 83Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Process Capability Natural tolerance limits are defined as follows:

4. Chapter 84Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Uses of process capability data:

5. Chapter 8 5 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Process may have good potential capability Reasons for Poor Process Capability

6. Chapter 86Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

7. Chapter 87Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

8. Chapter 88Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

9. Chapter 89Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Probability Plotting

10. Chapter 810Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. The distribution may not be normal; other types of probability plots can be useful in determining the appropriate distribution.

11. Chapter 811Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

12. Chapter 812Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

13. Chapter 813Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. For the hard bake process:

14. Chapter 814Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. One-Sided PCR

15. Chapter 815Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Interpretation of the PCR

16. Chapter 816Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Violation of these assumptions can lead to big trouble in using the data in Table 8.2. Assumptions for Interpretation of Numbers in Table 8.2

17. Chapter 817Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

18. Chapter 818Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. C p does not take process centering into account It is a measure of potential capability, not actual capability

19. Chapter 819Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. A Measure of Actual Capability

20. Chapter 820Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Normality and Process Capability Ratios The assumption of normality is critical to the usual interpretation of these ratios (such as Table 8.2) For non-normal data, options are 1.Transform non-normal data to normal 2.Extend the usual definitions of PCRs to handle non-normal data 3.Modify the definitions of PCRs for general families of distributions

21. Chapter 821Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Other Types of Process Capability Ratios 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

22. Chapter 822Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

23. Chapter 823Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

24. Chapter 824Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

25. Chapter 825Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

26. Chapter 826Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

27. Chapter 827Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

28. Chapter 828Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Process Capability Analysis using Control Charts

29. Chapter 829Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Since LSL = 200

30. Chapter 830Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

31. Chapter 831Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

32. Chapter 832Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

33. Chapter 833Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

34. Chapter 834Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. 7.8 Gauge and Measurement Systems Capability Studies Determine how much of the observed variability is due to the gauge or measurement system Isolate the components of variability in the measurement system Assess whether the gauge is capable (suitable for the intended application)

35. Chapter 835Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

36. Chapter 836Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

37. Chapter 837Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

38. Chapter 838Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. The P/T ratio:

39. Chapter 839Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

40. Chapter 840Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Estimating the Variance Components

41. Chapter 841Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

42. Chapter 842Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. The gauge is not capable by this criterion

43. Chapter 843Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Discrimination Ratio

44. Chapter 844Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Accuracy and Precision We have focused only on precision

45. Chapter 845Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Gauge R&R Studies

46. Chapter 846Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Gauge R&R Studies Are Usually Conducted with a Factorial Experiment

47. Chapter 847Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. This is a two-factor factorial experiment ANOVA methods are used to analyze the data and yo estimate the variance components

48. Chapter 848Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

49. Chapter 849Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

50. Chapter 850Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

51. Chapter 851Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

52. Chapter 852Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Negative estimates of a variance component would lead to filling a reduced model, such as, for example:

53. Chapter 853Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

54. Chapter 854Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. For this Example

55. Chapter 855Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Other Topics in Gauge R&R Studies Section 8.7.3 provides a description of methods to obtain confidence intervals on the variance components and measures of gauge R&R Section 8.7.4 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

56. Chapter 856Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. 8.7.5 Attribute Gauge Capability Sometimes the output of a gauge isn’t numerical – it’s just pass/fail Nominal or ordinal data is also common Occurs frequently in service businesses Common situation – do operating personnel consistently make the same decisions regarding the units they are inspecting or analyzing Example – a bank uses manual underwriting of mortgage loans The underwriter uses information to classify the applicant into one of four categories; decline or category 1, 2, 3 – categories 2 & 3 are low-risk and 1 is high risk Compare underwriters performance relative to a “consensus” evaluation determined by a panel of “experts”

57. Chapter 8 57 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Thirty applicants, three underwriters Each underwriter evaluates each application twice The applications are “blinded” by removing names, SSNs, addresses, and other identifying information

58. Chapter 858Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Attribute Gauge Capability Determine the proportion of time that the underwriter agrees with him/herself – this measures repeatability Determine the proportion of time that the underwriter agrees with the correct classification – this measures bias Minitab performs the analysis – using the attribute agreement analysis routine

59. Chapter 859Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

60. Chapter 860Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

61. Chapter 861Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

62. Chapter 862Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

63. Chapter 863Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

64. Chapter 864Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

65. Chapter 865Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. 8.8 Setting Specifications on Discrete Components Components interact with other components Complex assemblies Tolerance stack-up problems Linear combinations Nonlinear combinations

66. Chapter 866Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

67. Chapter 867Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

68. Chapter 868Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

69. Chapter 8 69 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

70. Chapter 870Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

71. Chapter 871Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

72. Chapter 872Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Difference between tolerance limits and confidence limits Nonparametric tolerance limits can also be calculated 8.9 Estimating the Natural Tolerance Limits of a Process For a normal distribution with unknown mean and variance:

73. Chapter 873Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

74. Chapter 874Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

75. Chapter 875Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Learning Objectives