Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc.
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1 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 1
2 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 2
3 Learning Objectives Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 3
4 Process Capability Natural tolerance limits are defined as follows: Chapter 8 4
5 Uses of process capability data: Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 5
6 Reasons for Poor Process Capability Process may have good potential capability Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 6
7 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 7
8 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 8
9 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 9
10 Probability Plotting Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 10
11 The distribution may not be normal; other types of probability plots can be useful in determining the appropriate distribution. ib ti Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 11
12 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 12
13 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 13
14 For the hard bake process: Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 14
15 One-Sided PCR Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 15
16 Interpretation of the PCR Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 16
17 Assumptions for Interpretation of Numbers in Tbl Table Violation of these assumptions can lead to big trouble in using the data in Table 8.2. Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 17
18 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 18
19 C p does not take process centering into account It is a measure of potential capability, not actual capability Chapter 8 19
20 A Measure of Actual Capability Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 20
21 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 ldata 3. Modify the definitions of PCRs for general families of distributions Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 21
22 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 sg extent e in practice ce Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 22
23 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 23
24 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 24
25 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 25
26 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 26
27 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 27
28 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 28
29 Process Capability Analysis using Control Charts Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 29
30 Since LSL = 200 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 30
31 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 31
32 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 32
33 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 33
34 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 34
35 8.7 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) Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 35
36 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 36
37 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 37
38 Chapter 8 38
39 The P/T (precision-to-tolerance) ratio: Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 39
40 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 40
41 Estimating the Variance Components Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 41
42 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 42
43 The gauge is not capable by this criterion Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 43
44 Discrimination Ratio Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 44
45 Accuracy and Precision We have focused only on precision Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 45
46 Gauge R&R Studies Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 46
47 Gauge R&R Studies Are Usually Conducted with a Factorial Experiment Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 47
48 This is a two-factor factorial experiment ANOVA methods are used to analyze the data and to estimate the variance components Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 48
49 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 49
50 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 50
51 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 51
52 Negative estimates of a variance component would lead to filling a reduced model, such as, for example: Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 52
53 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 53
54 For this Example Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 54
55 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 gg good units (producer s risk) Passing bad units (consumer s risk) Methods for calculating these two probabilities are given Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 55
56 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 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 56
57 Thirty applicants, three underwriters Each underwriter evaluates each application twice The applications are blinded by removing names, SSNs, addresses, and other identifying information Chapter 8 57
58 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 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 58
59 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 59
60 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 60
61 8.8 Setting Specifications on Discrete Components Components interact with other components Complex assemblies Tolerance stack-up problems Linear combinations Nonlinear combinations Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 61
62 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 62
63 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 63
64 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 64
65 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 65
66 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 66
67 8.9 Estimating the Natural Tolerance Limits i of a Process For a normal distribution with unknown mean and variance: Difference between tolerance limits and confidence limits Nonparametric tolerance limits can also be calculated Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 67
68 Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 68
69 Learning Objectives Chapter 8 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. 69
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