The multivariate solution to statistical process control : qualstat 3

Title:

Personal Author:

Mason, Robert Lee, 1946-

Series:

ASA-SIAM series on statistics and applied probability

Publication Information:

Philadelphia, PA : Society for Industrial and Applied Mathematics, 2002

Physical Description:

1 CD-ROM ; 12 cm

ISBN:

9780898714968

General Note:

Accompanies text entitled : Multivariate statistical process control with industrial applications (TS156.8 M37 2002)

Subject Term:

Process control -- Statistical methods

Added Author:

Young, John C., 1942-

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This applied, self-contained text provides detailed coverage of the practical aspects of multivariate statistical process control (MVSPC) based on the application of Hotelling's T2 statistic. MVSPC is the application of multivariate statistical techniques to improve the quality and productivity of an industrial process. The authors, leading researchers in this area who have developed major software for this type of charting procedure, provide valuable insight into the T2 statistic. Intentionally including only a minimal amount of theory, they lead readers through the construction and monitoring phases of the T2 control statistic using numerous industrial examples taken primarily from the chemical and power industries. These examples are applied to the construction of historical data sets to serve as a point of reference for the control procedure and are also applied to the monitoring phase, where emphasis is placed on signal location and interpretation in terms of the process variables.

Specifically devoted to the T2 methodology, this is the only book available that concisely and thoroughly presents such topics as how to construct a historical data set; how to check the necessary assumptions used with this procedure; how to chart the T2 statistic; how to interpret its signals; how to use the chart in the presence of autocorrelated data; and how to apply the procedure to batch processes. The book comes with a CD-ROM containing a 90-day demonstration version of the QualStat™ multivariate SPC software specifically designed for the application of T2 control procedures. The CD-ROM is compatible with Windows® 95, Windows® 98, Windows® Me Millennium Edition, and Windows NT® operating systems.

Author Notes

Robert L. Mason is a Staff Analyst at the Southwest Research Institute in San Antonio, Texas. He is a fellow of both the American Statistical Association and the American Society for Quality
John C. Young is a Professor of Statistics at McNeese State University in Lake Charles, Louisiana

Preface	p. xi
1 Introduction to the T[superscript 2] Statistic	p. 1
1.1 Introduction	p. 3
1.2 Univariate Control Procedures	p. 4
1.3 Multivariate Control Procedures	p. 5
1.4 Characteristics of a Multivariate Control Procedure	p. 9
1.5 Summary	p. 11
2 Basic Concepts about the T[superscript 2] Statistic	p. 13
2.1 Introduction	p. 13
2.2 Statistical Distance	p. 13
2.3 T[superscript 2] and Multivariate Normality	p. 17
2.4 Student t versus Hotelling's T[superscript 2]	p. 20
2.5 Distributional Properties of the T[superscript 2]	p. 22
2.6 Alternative Covariance Estimators	p. 26
2.7 Summary	p. 28
2.8 Appendix: Matrix Algebra Review	p. 28
2.8.1 Vector and Matrix Notation	p. 29
2.8.2 Data Matrix	p. 29
2.8.3 The Inverse Matrix	p. 30
2.8.4 Symmetric Matrix	p. 30
2.8.5 Quadratic Form	p. 31
2.8.6 Wishart Distribution	p. 32
3 Checking Assumptions for Using a T[superscript 2] Statistic	p. 33
3.1 Introduction	p. 33
3.2 Assessing the Distribution of the T[superscript 2]	p. 33
3.3 The T[superscript 2] and Nonnormal Distributions	p. 37
3.4 The Sampling Distribution of the T[superscript 2] Statistic	p. 37
3.5 Validation of the T[superscript 2] Distribution	p. 41
3.6 Transforming Observations to Normality	p. 47
3.7 Distribution-Free Procedures	p. 48
3.8 Choice of Sample Size	p. 49
3.9 Discrete Variables	p. 50
3.10 Summary	p. 50
3.11 Appendix: Confidence Intervals for UCL	p. 51
4 Construction of Historical Data Set	p. 53
4.1 Introduction	p. 54
4.2 Planning	p. 55
4.3 Preliminary Data	p. 57
4.4 Data Collection Procedures	p. 61
4.5 Missing Data	p. 62
4.6 Functional Form of Variables	p. 64
4.7 Detecting Collinearities	p. 65
4.8 Detecting Autocorrelation	p. 68
4.9 Example of Autocorrelation Detection Techniques	p. 72
4.10 Summary	p. 78
4.11 Appendix	p. 78
4.11.1 Eigenvalues and Eigenvectors	p. 78
4.11.2 Principal Component Analysis	p. 79
5 Charting the T[superscript 2] Statistic in Phase I	p. 81
5.1 Introduction	p. 81
5.2 The Outlier Problem	p. 81
5.3 Univariate Outlier Detection	p. 82
5.4 Multivariate Outlier Detection	p. 85
5.5 Purging Outliers: Unknown Parameter Case	p. 86
5.5.1 Temperature Example	p. 86
5.5.2 Transformer Example	p. 89
5.6 Purging Outliers: Known Parameter Case	p. 91
5.7 Unknown T[superscript 2] Distribution	p. 92
5.8 Summary	p. 96
6 Charting the T[superscript 2] Statistic in Phase II	p. 97
6.1 Introduction	p. 98
6.2 Choice of False Alarm Rate	p. 98
6.3 T[superscript 2] Charts with Unknown Parameters	p. 100
6.4 T[superscript 2] Charts with Known Parameters	p. 105
6.5 T[superscript 2] Charts with Subgroup Means	p. 106
6.6 Interpretive Features of T[superscript 2] Charting	p. 108
6.7 Average Run Length (Optional)	p. 111
6.8 Plotting in Principal Component Space (Optional)	p. 115
6.9 Summary	p. 118
7 Interpretation of T[superscript 2] Signals for Two Variables	p. 119
7.1 Introduction	p. 119
7.2 Orthogonal Decompositions	p. 120
7.3 The MYT Decomposition	p. 125
7.4 Interpretation of a Signal on a T[superscript 2] Component	p. 127
7.5 Regression Perspective	p. 129
7.6 Distribution of the T[superscript 2] Components	p. 131
7.7 Data Example	p. 135
7.8 Conditional Probability Functions (Optional)	p. 140
7.9 Summary	p. 142
7.10 Appendix: Principal Component Form of T[superscript 2]	p. 143
8 Interpretation of T[superscript 2] Signals for the General Case	p. 147
8.1 Introduction	p. 147
8.2 The MYT Decomposition	p. 147
8.3 Computing the Decomposition Terms	p. 149
8.4 Properties of the MYT Decomposition	p. 152
8.5 Locating Signaling Variables	p. 155
8.6 Interpretation of a Signal on a T[superscript 2] Component	p. 157
8.7 Regression Perspective	p. 162
8.8 Computational Scheme (Optional)	p. 163
8.9 Case Study	p. 165
8.10 Summary	p. 169
9 Improving the Sensitivity of the T[superscript 2] Statistic	p. 171
9.1 Introduction	p. 172
9.2 Alternative Forms of Conditional Terms	p. 172
9.3 Improving Sensitivity to Abrupt Process Changes	p. 174
9.4 Case Study: Steam Turbine	p. 175
9.4.1 The Control Procedure	p. 175
9.4.2 Historical Data Set	p. 176
9.5 Model Creation Using Expert Knowledge	p. 180
9.6 Model Creation Using Data Exploration	p. 183
9.7 Improving Sensitivity to Gradual Process Shifts	p. 188
9.8 Summary	p. 191
10 Autocorrelation in T[superscript 2] Control Charts	p. 193
10.1 Introduction	p. 193
10.2 Autocorrelation Patterns in T[superscript 2] Charts	p. 194
10.3 Control Procedure for Uniform Decay	p. 199
10.4 Example of a Uniform Decay Process	p. 201
10.4.1 Detection of Autocorrelation	p. 202
10.4.2 Autoregressive Functions	p. 202
10.4.3 Estimates	p. 207
10.4.4 Examination of New Observations	p. 209
10.5 Control Procedure for Stage Decay Processes	p. 211
10.6 Summary	p. 212
11 The T[superscript 2] Statistic and Batch Processes	p. 213
11.1 Introduction	p. 213
11.2 Types of Batch Processes	p. 213
11.3 Estimation in Batch Processes	p. 217
11.4 Outlier Removal for Category 1 Batch Processes	p. 219
11.5 Example: Category 1 Batch Process	p. 221
11.6 Outlier Removal for Category 2 Batch Processes	p. 226
11.7 Example: Category 2 Batch Process	p. 226
11.8 Phase II Operation with Batch Processes	p. 230
11.9 Example of Phase II Operation	p. 232
11.10 Summary	p. 234
Appendix Distribution Tables	p. 237
Bibliography	p. 253
Index	p. 259

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