Advanced Topics in Statistical Process Control The Power of Shewhart's Charts Donald J. Wheeler

SPC Press, Inc.
5908 Toole Drive, Suite C Knoxville, Tennessee 37919
(615) 584-5005 Fax(615) 588-9440
ISBN 0-945320-45-0
xiv + 470 pages

Contents

Preface

The Shewhart Catechism

Chapter One Shewhart's Control Charts

1.1 Shewhart's Definition of Statistical Control
1.2 Shewhart's "Operation of Statistical Control"
1.3 The Four Possibilities for Any Process
1.4 Control Charts and the Probability Approach
1.5 Enumerative Studies and Analytic Studies
1.6 The Uses of Shewhart's Charts
1.7 The Four Foundations of Shewhart's Charts
1.8 Control Charts and Chaos Theory
1.9 The Transformation of Data

Chapter Two Statistics Versus Parameters

2.1 Measures of Location and Dispersion
2.2 The Notion of a Probability Distribution
2.3 Statistics, Parameters, and Control Chart Limits
2.4 Skewness and Kurtosis

Chapter Three Estimating Dispersion Parameters

3.1 Estimators of SD(X) and V(X) for One Subgroup of Size n
3.2 Three Ways to Estimate SD(X) for k Subgroups of Size n
3.3 The Second Foundation of Shewhart's Charts
3.4 Within-Subgroup Estimates of Dispersion
3.5 Time Series Data (Subgroups of Size One)
3.6 Degrees of Freedom
3.7 Summary

Chapter Four Control Charts for Measurements

4.1 Average and Range Charts
4.2 Average and Root Mean Square Deviation Charts
4.3 Average and Standard Deviation Charts
4.4 Average and Variance Charts
4.5 So What's the Difference?
4.6 Charts for Individual Values
4.7 Median and Range Charts

Chapter Five Three Sigma Limits

5.1 Why Three-Sigma Limits?
5.2 But What About the Central Limit Theorem?
5.3 The Recalculation of Control Limits
5.4 The Role of the Normal Distribution
5.5 Calculating Limits With Small Amounts of Data
5.6 Inadequate Measurement Units
5.7 Detecting a Lack of Control
5.8 Summary

Chapter Six Rational Sampling and Rational Subgrouping

6.1 Rational Sampling
6.2 Rational Subgrouping
6.3 Principles for Subgrouping
6.4 Three-Way Control Charts
6.5 Summary

Chapter Seven The Quality of Control Limits

7.1 The Distribution of the Average Range Statistic
7.2 The Distribution of the Average Root Mean Square Statistic
7.3 The Distribution of the Average Standard Deviation Statistic
7.4 The Distribution of the Pooled Variance Statistic
7.5 The Distribution of the Median Range Statistic
7.6 The Distribution of the Average Moving Range
7.7 Degrees of Freedom
7.8 Effective Degrees of Freedom
7.9 Using Degrees of Freedom
7.10 The Quality of Control Limits
7.11 Summary

Chapter Eight Capability Confusion

8.1 Capability, Capability Ratios, and Performance Ratios
8.2 The Capability of a Stable Process
8.3 Capability Measures
8.4 Converting Capabilities Into Fraction Nonconforming
8.5 Performance Ratios
8.6 World-Class Quality
8.7 Summary

Chapter Nine Power Functions for Control Charts

9.1 The Power of Charts for Location
9.2 The Formulas for the Power Functions
9.3 The Average Run Length for a Procedure
9.4 Summary

Chapter Ten Comparing Different Types of Control Charts

10.1 Control Charts for Subgroup Averages
10.2 Control Charts for Moving Averages
10.3 Moving Averages or Individual Values?
10.4 Contra Two-Sigma Limits
10.5 Summary

Chapter Eleven Control Charts for Count Data

11.1 Control Charts for Count Data
11.2 np-Charts
11.3 p-Charts
11.4 A Problem With Binomial Counts
11.5 c-Charts
11.6 u-Charts
11.7 A Problem With Poisson Counts
11.8 Degrees of Freedom
11.9 Control Charts for Rare Events
11.10 Summary

Chapter Twelve Control Charts for Autocorrelated Data

12.1 Correlation
12.2 Significant Correlations
12.3 Autocorrelation
12.4 What Does Autocorrelation Say About the Process?
12.5 The Effect of Autocorrelation
12.6 Autocorrelation's Effect Upon Control Limits
12.7 So What Shall I Do With My Autocorrelated Data?

Chapter Thirteen The Cumulative Sum Technique

13.1 Cumulative Sums for Individual Values
13.2 Cumulative Sums for Subgroup Averages
13.3 Average Run Lengths for Selected Cusum Procedures
13.4 Summary

Chapter Fourteen Exponentially Weighted Moving Averages

14.1 The EWMA Algorithm
14.2 EWMA for Individual Values
14.3 Average Run Lengths for the EWMA
14.4 Then What Does an EWMA Do?
14.5 Summary

Chapter Fifteen Multivariate Charts

15.1 Simple Multivariate Control Charts
15.2 Control Charts for Hotelling's T2 Statistic

Chapter Sixteen Miscellaneous Techniques

16.1 Zone Charts
16.2 Modified Control Charts
16.3 PreControl
16.4 Summary

Chapter Seventeen The Characterization of Product

17.1 Characterizing the Measured Item
17.2 Characterizing Product Which Has Not Been Measured
17.3 The Fallacy of Acceptance Sampling
17.4 Estimating the Fraction Nonconforming
17.5 Summary

Chapter Eighteen The Analysis of Means

18.1 Comparing k Treatments Using Control Charts
18.2 Experimental Data vs. Production Data
18.3 The Decision Limits for ANOM
18.4 The Role of the Range Chart with ANOM
18.5 ANOM With Multifactor Studies
18.6 Interaction Effects and ANOM
18.7 ANOM With Unequal Subgroup Sizes
18.8 The Analysis of Mean Ranges
18.9 Summary

Chapter Nineteen Some Differences Between Theory and Practice

19.1 The Scientific Process
19.2 Statistical Tests of Hypotheses
19.3 Enumerative Studies
19.4 Analytical Studies
19.5 Shewhart on Probability Models and Processes
19.6 Finding Decision Rules for Analytic Studies
19.7 Conclusions

Appendix

Glossary of Symbols

Bibliography

Tables
Table 1: Bias Correction Factors
Table 2: Bias Correction Factors for Estimating V(X)
Table 3: Individual Values Charts
Table 4: Average and Range Charts Using the Average Range
Table 5: Average and Range Charts Using the Median Range
Table 6: Average and Range Charts Based on Sigma(X)
Table 7: Average and RMS Dev. Charts Using Average RMS Dev.
Table 8: Average and RMS Dev. Charts Using Median RMS Dev.
Table 9: Average and RMS Dev. Charts Based on Sigma(X)
Table 10: Average and Std. Dev. Charts Using Average Std. Dev.
Table 11: Average and Std. Dev. Charts Using Median Std. Dev.
Table 12: Average and Std. Dev. Charts Based on Sigma(X)
Table 13: Average and Std. Dev. Charts Using Pooled Variance
Table 14: Median and Range Charts Using the Average Range
Table 15: Median and Range Charts Using the Median Range
Table 16: Median and Range Charts Based on Sigma(X)
Table 17: Average and Variance Charts
Table 18: Moments for Range Distributions
Table 19: Moments for Distributions of the RMS Deviation
Table 20: Moments for Distributions of the Standard Deviation
Table 21: Degrees of Freedom for Average Ranges
Table 22: Degrees of Freedom for Median Ranges
Table 23: Degrees of Freedom for Average Moving Ranges
Table 24: Degrees of Freedom for Median Moving Ranges
Table 25: Degrees of Freedom for Average Std. Dev. and RMS Dev.
Table 26: Degrees of Freedom for Median Std. Dev. and RMS Dev.
Table 27: The Standard Normal Distribution
Table 28: ANOM Critical Values
Table 29: Critical Values for Analysis of Mean Ranges (ANOMR)
Table 30: Central Lines and Upper Limits for Hotelling's T2
Table 31: 37 Reference Tables and Figures Located Within Text

Index