Multivariate statistical methods in quality management

Title:

Personal Author:

Yang, Kai

Publication Information:

New York : McGraw-Hill 2004

ISBN:

9780071432085

Subject Term:

Quality control -- Statistical methods

Multivariate analysis

Added Author:

Trewn, Jayant

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UPGRADE MANUFACTURING AND SERVICE PERFORMANCE WITH POWERFUL STATISTICAL TOOLS

There's no better way to master the most rigorous statistical methods available for analyzing the performance of complex systems -- Multivariate Statistical Methods in Quality Management teaches powerful analytic tools for troubleshooting, root cause analysis, process control, quality improvement, and many other applications. Written by statistics experts who specialize in reliability and quality engineering, this unique resource introduces the fundamentals and then demonstrates how to:

*Choose the best method for each data set
* Make complex data intelligible with graphical tools
* Coax important hidden information from data with graphical 3-D software and numerical multivariate data stratification
* Perform data reduction with principal component analysis, factor analysis, and discriminant analysis
* Apply multivariate methods in Six Sigma enterprises
* Get clarification from case studies, models, and 50 illustrations
* Uncover the source of problems and pinpoint solutions in arenas from manufacturing processes to sales performance and beyond

Author Notes

Kai Yang, Ph.D., has consulted extensively in many areas of quality and reliability engineering. He is Associate Professor of Industrial and Manufacturing Engineering at Wayne State University, Detroit, Michigan
Jayant Trewn, Ph.D., is a research faculty member at Beaumont Hospital in Royal Oak Michigan

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Yang (Wayne State Univ.) and Trewn (Beaumont Hospital, Royal Oak, Michigan) describe applications of multivariate statistical techniques for those in industry and business who work with problems of quality management and reliability. Chapter 1 overviews multivariate statistical methods and use in quality assurance practice and Six Sigma projects; chapter 2 applies graphs and data stratification to problem solving. Chapters 3 and 4 include material on multivariate random variables, multivariate normal distribution, sampling properties, and multivariate analysis of variance. Principal component analysis and factor analysis, two very important and useful multivariate statistical techniques, are discussed in detail in chapter 5. Discriminant analysis, a very powerful method for classifying objects into groups, is discussed in chapter 6, while chapter 7 includes material on cluster analysis. Taguchi techniques and Mahalanobis distance, with their applications to quality control, are presented in chapter 8 along with alternative approaches. Chapter 9 treats path analysis and the structural model, and the last chapter discusses multivariate statistical process control, including discussion of some popular multivariate control charts. Readers need familiarity with matrix algebra and statistical methods for analyzing data of one random variable. This excellent and very valuable book includes numerous practical examples and case studies. ^BSumming Up: Highly recommended. Upper-division undergraduates through professionals. D. V. Chopra Wichita State University

Preface	p. xiii
Chapter 1. Multivariate Statistical Methods and Quality	p. 1
1.1 Overview of Multivariate Statistical Methods	p. 1
1.1.1 Graphical multivariate data display and data stratification	p. 3
1.1.2 Multivariate normal distribution and multivariate sampling distribution	p. 3
1.1.3 Multivariate analysis of variance	p. 4
1.1.4 Principal component analysis and factor analysis	p. 5
1.1.5 Discriminant analysis	p. 6
1.1.6 Cluster analysis	p. 7
1.1.7 Mahalanobis Taguchi system (MTS)	p. 7
1.1.8 Path analysis and structural model	p. 8
1.1.9 Multivariate process control	p. 10
1.2 Applications of Multivariate Statistical Methods in Business and Industry	p. 10
1.2.1 Data mining	p. 11
1.2.2 Chemometrics	p. 12
1.2.3 Other applications	p. 13
1.3 Overview of Quality Assurance and Possible Roles of Multivariate Statistical Methods	p. 13
1.3.1 Stage 0: Impetus/ideation	p. 13
1.3.2 Stage 1: Customer and business requirements study	p. 15
1.3.3 Stage 2: Concept development	p. 15
1.3.4 Stage 3: Product/service design/prototyping	p. 15
1.3.5 Stage 4: Manufacturing process preparation/product launch	p. 16
1.3.6 Stage 5: Production	p. 16
1.3.7 Stage 6: Product/service consumption	p. 17
1.3.8 Stage 7: Disposal	p. 17
1.4 Overview of Six Sigma and Possible Roles of Multivariate Statistical Methods	p. 18
1.4.1 Stage 1: Define the project and customer requirements (D or define step)	p. 20
1.4.2 Stage 2: Measuring process performance	p. 21
1.4.3 Stage 3: Analyze data and discover causes of the problem	p. 21
1.4.4 Stage 4: Improve the process	p. 22
1.4.5 Stage 5: Control the process	p. 23
Chapter 2. Graphical Multivariate Data Display and Data Stratification	p. 25
2.1 Introduction	p. 25
2.2 Graphical Templates for Multivariate Data	p. 26
2.2.1 Charts and graphs	p. 26
2.2.2 Templates for displaying multivariate data	p. 29
2.3 Data Visualization and Animation	p. 33
2.3.1 Introduction to data visualization	p. 33
2.4 Multivariate Data Stratification	p. 38
2.4.1 Multi-vari chart technique	p. 39
2.4.2 Graphical analysis of multivariate variation pattern	p. 41
Chapter 3. Introduction to Multivariate Random Variables, Normal Distribution, and Sampling Properties	p. 47
3.1 Overview of Multivariate Random Variables	p. 47
3.2 Multivariate Data Sets and Descriptive Statistics	p. 50
3.2.1 Multivariate data sets	p. 50
3.2.2 Multivariate descriptive statistics	p. 51
3.3 Multivariate Normal Distributions	p. 55
3.3.1 Some properties of the multivariate normal distribution	p. 56
3.4 Multivariate Sampling Distribution	p. 57
3.4.1 Sampling distribution of X	p. 57
3.4.2 Sampling distribution of S	p. 58
3.4.3 Central limit theorem applied to multivariate samples	p. 58
3.4.4 Hotelling's T[superscript 2] distribution	p. 59
3.4.5 Summary	p. 60
3.5 Multivariate Statistical Inferences on Mean Vectors	p. 60
3.5.1 Small sample multivariate hypothesis testing on a mean vector	p. 62
3.5.2 Large sample multivariate hypothesis testing on a mean vector	p. 63
3.5.3 Small sample multivariate hypothesis testing on the equality of two mean vectors	p. 64
3.5.4 Large sample multivariate hypothesis testing on the equality of two mean vectors	p. 66
3.5.5 Overview of confidence intervals and confidence regions in multivariate statistical inferences	p. 67
3.5.6 Confidence regions and intervals for a single mean vector with small sample size	p. 68
3.5.7 Confidence regions and intervals for a single mean vector with large sample size	p. 70
3.5.8 Confidence regions and intervals for the difference in two population mean vectors for small samples	p. 71
3.5.9 Confidence regions and intervals for the difference in two population mean vectors for large samples	p. 72
3.5.10 Other Cases	p. 73
Appendix 3A Matrix Algebra Refresher	p. 73
A.1 Introduction	p. 73
A.2 Notations and basic operations	p. 73
A.3 Matrix operations	p. 75
Chapter 4. Multivariate Analysis of Variance	p. 81
4.1 Introduction	p. 81
4.2 Univariate Analysis of Variance (ANOVA)	p. 82
4.2.1 The ANOVA table	p. 85
4.3 Multivariate Analysis of Variance	p. 86
4.3.1 MANOVA model	p. 86
4.3.2 The decomposition of total variation under MANOVA model	p. 88
4.4 MANOVA Case Study	p. 95
Chapter 5. Principal Component Analysis and Factor Analysis	p. 97
5.1 Introduction	p. 97
5.2 Principal Component Analysis Based on Covariance Matrices	p. 99
5.2.1 Two mathematical representations of principal component analysis	p. 100
5.2.2 Properties of principal component analysis	p. 101
5.2.3 Covariance and correlation between X and principal components Y	p. 103
5.2.4 Principal component analysis on sample covariance matrix	p. 103
5.3 Principal Component Analysis Based on Correlation Matrices	p. 108
5.3.1 Principal component scores and score plots	p. 111
5.4 Principal Component Analysis of Dimensional Measurement Data	p. 114
5.4.1 Properties of the geometrical variation mode	p. 117
5.4.2 Variation mode chart	p. 118
5.4.3 Visual display and animation of principal component analysis	p. 121
5.4.4 Applications for other multivariate data	p. 122
5.5 Principal Component Analysis Case Studies	p. 124
5.5.1 Improving automotive dimensional quality by using principal component analysis	p. 124
5.5.2 Performance degradation analysis for IRLEDs (Yang and Yang, 2000)	p. 131
5.6 Factor Analysis	p. 141
5.6.1 Common factor analysis	p. 143
5.6.2 Properties of common factor analysis	p. 143
5.6.3 Parameter estimation in common factor analysis	p. 147
5.7 Factor Rotation	p. 148
5.7.1 Factor rotation for simple structure	p. 149
5.7.2 Procrustes rotation	p. 152
5.8 Factor Analysis Case Studies	p. 152
5.8.1. Characterization of texture and mechanical properties of heat-induced soy protein gels (Kang, Matsumura, and Mori, 1991)	p. 152
5.8.2 Procrustes factor analysis for automobile body assembly process	p. 154
5.8.3 Hinge variation study using procrustes factor analysis	p. 156
Chapter 6. Discriminant Analysis	p. 161
6.1 Introduction	p. 161
6.1.1 Discriminant analysis steps	p. 162
6.2 Linear Discriminant Analysis for Two Normal Populations with Known Covariance Matrix	p. 163
6.3 Linear Discriminant Analysis for Two Normal Population with Equal Covariance Matrices	p. 167
6.4 Discriminant Analysis for Two Normal Population with Unequal Covariance Matrices	p. 169
6.5 Discriminant Analysis for Several Normal Populations	p. 170
6.5.1 Linear discriminant classification	p. 170
6.5.2 Discriminant classification based on the Mahalanobis squared distances	p. 171
6.6 Case Study: Discriminant Analysis of Vegetable Oil by Near-Infrared Reflectance Spectroscopy	p. 175
Chapter 7. Cluster Analysis	p. 181
7.1 Introduction	p. 181
7.2 Distance and Similarity Measures	p. 183
7.2.1 Euclidean distance	p. 183
7.2.2 Standardized euclidean distance	p. 183
7.2.3 Manhattan distance (city block distance)	p. 184
7.2.4 Distance between clusters and linkage method	p. 185
7.2.5 Similarity	p. 189
7.3 Hierarchical Clustering Method	p. 190
7.4 Nonhierarchical Clustering Method (K-Mean Method)	p. 195
7.5 Cereal Brand Case Study	p. 197
Chapter 8. Mahalanobls Distance and Taguchi Method	p. 201
8.1 Introduction	p. 201
8.2 Overview of the Mahalanobis-Taguchi System (MTS)	p. 202
8.2.1 Stage 1: Creation of a baseline Mahalanobis space	p. 203
8.2.2 Stage 2: Test and analysis of the Mahalanobis measure for abnormal samples	p. 205
8.2.3 Stage 3 variable screening by using Taguchi orthogonal array experiments	p. 206
8.2.4 Stage 4: Establish a threshold value (a cutoff MD) based on Taguchi's quality loss function and maintain a multivariate monitoring system	p. 214
8.3 Features of the Mahalanobis-Taguchi System	p. 216
8.4 The Mahalanobis-Taguchi System Case Study	p. 216
8.4.1 Clutch disc inspection	p. 217
8.5 Comments on the Mahalanobis-Taguchi System by Other Researchers and Proposed Alternative Approaches	p. 221
8.5.1 Alternative approaches	p. 221
Chapter 9. Path Analysis and the Structural Model	p. 223
9.1 Introduction	p. 223
9.2 Path Analysis and the Structural Model	p. 225
9.2.1 How to use the path diagram and structural model	p. 228
9.3 Advantages and Disadvantages of Path Analysis and the Structural Model	p. 235
9.3.1 Advantages	p. 235
9.3.2 Disadvantages	p. 236
9.4 Path Analysis Case Studies	p. 237
9.4.1 Path analysis model relating plastic fuel tank characteristics with its hydrocarbon permeation (Hamade, 1996)	p. 237
9.4.2 Path analysis of a foundry process (Price and Barth, 1995)	p. 241
Chapter 10. Multivariate Statistical Process Control	p. 243
10.1 Introduction	p. 243
10.2 Multivariate Control Charts for Given Targets	p. 245
10.2.1 Decomposition of the Hotelling T[superscript 2]	p. 248
10.3 Two-Phase T[superscript 2] Multivariate Control Charts with Subgroups	p. 251
10.3.1 Reference sample and new observations	p. 251
10.3.2 Two-phase T[superscript 2] multivariate process control for subgroups	p. 255
10.4 T[superscript 2] Control Chart for Individual Observations	p. 259
10.4.1 Phase I reference sample preparation	p. 260
10.4.2 Phase II: Process control for new observations	p. 264
10.5 Principal Component Chart	p. 265
Appendix Probability Distribution Tables	p. 271
References	p. 291
Index	p. 295

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