Multivariate Statistical Methods in Quality Management

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ISBN: 9780071432085 | 0071432086
Cover: Hardcover
Copyright: 3/17/2004

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Multivariate statistical methods are an essential component of quality engineering data analysis. This monograph provides a solid background in multivariate statistical fundamentals and details key multivariate statistical methods, including simple multivariate data graphical display and multivariate data stratification. * Graphical multivariate data display * Multivariate regression and path analysis * Multivariate process control charts * Six sigma and multivariate statistical methods

Preface

xiii

Chapter 1. Multivariate Statistical Methods and Quality

(24)

1.1 Overview of Multivariate Statistical Methods

(9)

1.1.1 Graphical multivariate data display and data stratification

(1)

1.1.2 Multivariate normal distribution and multivariate sampling distribution

(1)

1.1.3 Multivariate analysis of variance

(1)

1.1.4 Principal component analysis and factor analysis

(1)

1.1.5 Discriminant analysis

(1)

1.1.6 Cluster analysis

(1)

1.1.7 Mahalanobis Taguchi system (MTS)

(1)

1.1.8 Path analysis and structural model

(2)

1.1.9 Multivariate process control

(1)

1.2 Applications of Multivariate Statistical Methods In Business and Industry

(3)

1.2.1 Data mining

(1)

1.2.2 Chemometrics

(1)

1.2.3 Other applications

(1)

1.3 Overview of Quality Assurance and Possible Roles of Multivariate Statistical Methods

(5)

1.3.1 Stage 0: Impetus/ideation

(2)

1.3.2 Stage 1: Customer and business requirements study

(1)

1.3.3 Stage 2: Concept development

(1)

1.3.4 Stage 3: Product/service design/prototyping

(1)

1.3.5 Stage 4: Manufacturing process preparation/product launch

(1)

1.3.6 Stage 5: Production

(1)

1.3.7 Stage 6: Product/service consumption

(1)

1.3.8 Stage 7: Disposal

(1)

1.4 Overview of Six Sigma and Possible Roles of Multivariate Statistical Methods

(7)

1.4.1 Stage 1: Define the project and customer requirements (D or define step)

(1)

1.4.2 Stage 2: Measuring process performance

(1)

1.4.3 Stage 3: Analyze data and discover causes of the problem

(1)

1.4.4 Stage 4: Improve the process

(1)

1.4.5 Stage 5: Control the process

(2)

Chapter 2. Graphical Multivariate Data Display and Data Stratification

(22)

2.1 Introduction

(1)

2.2 Graphical Templates for Multivariate Data

(7)

2.2.1 Charts and graphs

(3)

2.2.2 Templates for displaying multivariate data

(4)

2.3 Data Visualization and Animation

(5)

2.3.1 Introduction to data visualization

(5)

2.4 Multivariate Data Stratification

(9)

2.4.1 Multi-vari chart technique

(2)

2.4.2 Graphical analysis of multivariate variation pattern

(6)

Chapter 3. Introduction to Multivariate Random Variables, Normal Distribution, and Sampling Properties

(34)

3.1 Overview of Multivariate Random Variables

(3)

3.2 Multivariate Data Sets and Descriptive Statistics

(5)

3.2.1 Multivariate data sets

(1)

3.2.2 Multivariate descriptive statistics

(4)

3.3 Multivariate Normal Distributions

(2)

3.3.1 Some properties of the multivariate normal distribution

(1)

3.4 Multivariate Sampling Distribution

(3)

3.4.1 Sampling distribution of X

(1)

3.4.2 Sampling distribution of S

(1)

3.4.3 Central limit theorem applied to multivariate samples

(1)

3.4.4 Hotelling's T-2 distribution

(1)

3.4.5 Summary

(1)

3.5 Multivariate Statistical Inferences on Mean Vectors

(13)

3.5.1 Small sample multivariate hypothesis testing on a mean vector

(1)

3.5.2 Large sample multivariate hypothesis testing on a mean vector

(1)

3.5.3 Small sample multivariate hypothesis testing on the equality of two mean vectors

(2)

3.5.4 Large sample multivariate hypothesis testing on the equality of two mean vectors

(1)

3.5.5 Overview of confidence intervals and confidence regions in multivariate statistical inferences

(1)

3.5.6 Confidence regions and intervals for a single mean vector with small sample size

(2)

3.5.7 Confidence regions and intervals for a single mean vector with large sample size

(1)

3.5.8 Confidence regions and intervals for the difference in two population mean vectors for small samples

(1)

3.5.9 Confidence regions and intervals for the difference In two population mean vectors for large samples

(1)

3.5.10 Other Cases

(1)

Appendix 3A: Matrix Algebra Refresher

(8)

A.1 Introduction

(1)

A.2 Notations and basic operations

(2)

A.3 Matrix operations

(6)

Chapter 4. Multivariate Analysis of Variance

(16)

4.1 Introduction

(1)

4.2 Univariate Analysis of Variance (ANOVA)

(4)

4.2.1 The ANOVA table

(1)

4.3 Multivariate Analysis of Variance

(9)

4.3.1 MANOVA model

(2)

4.3.2 The decomposition of total variation under MANOVA model

(7)

4.4 MANOVA Case Study

(2)

Chapter 5. Principal Component Analysis and Factor Analysis

(64)

5.1 Introduction

(2)

5.2 Principal Component Analysis Based on Covariance Matrices

(9)

5.2.1 Two mathematical representations of principal component analysis

100

(1)

5.2.2 Properties of principal component analysis

101

(2)

5.2.3 Covariance and correlation between X and principal components Y

103

(1)

5.2.4 Principal component analysis on sample covariance matrix

103

(5)

5.3 Principal Component Analysis Based on Correlation Matrices

108

(6)

5.3.1 Principal component scores and score plots

111

(3)

5.4 Principal Component Analysis of Dimensional Measurement Data

114

(10)

5.4.1 Properties of the geometrical variation mode

117

(1)

5.4.2 Variation mode chart

118

(3)

5.4.3 Visual display and animation of principal component analysis

121

(1)

5.4.4 Applications for other multivariate data

122

(2)

5.5 Principal Component Analysis Case Studies

124

(17)

5.5.1 Improving automotive dimensional quality by using principal component analysis

124

(7)

5.5.2 Performance degradation analysis for IRLEDs (Yang and Yang, 2000)

131

(10)

5.6 Factor Analysis

141

(7)

5.6.1 Common factor analysis

143

(1)

5.6.2 Properties of common factor analysis

143

(4)

5.6.3 Parameter estimation In common factor analysis

147

(1)

5.7 Factor Rotation

148

(4)

5.7.1 Factor rotation for simple structure

149

(3)

5.7.2 Procrustes rotation

152

(1)

5.8 Factor Analysis Case Studies

152

(9)

5.8.1 Characterization of texture and mechanical properties of heat-induced soy protein gels (Kang, Matsumura, and Mori, 1991)

152

(2)

5.8.2 Procrustes factor analysis for automobile body assembly process

154

(2)

5.8.3 Hinge variation study using procrustes factor analysis

156

(5)

Chapter 6. Discriminant Analysis

161

(20)

6.1 Introduction

161

(2)

6.1.1 Discriminant analysis steps

162

(1)

6.2 Linear Discriminant Analysis for Two Normal Populations with Known Covariance Matrix

163

(4)

6.3 Linear Discriminant Analysis for Two Normal Population with Equal Covariance Matrices

167

(2)

6.4 Discriminant Analysis for Two Normal Population with Unequal Covariance Matrices

169

(1)

6.5 Discriminant Analysis for Several Normal Populations

170

(5)

6.5.1 Linear discriminant classification

170

(1)

6.5.2 Discriminant classification based on the Mahalanobis squared distances

171

(4)

6.6 Case Study: Discriminant Analysis of Vegetable Oil by Near-Infrared Reflectance Spectroscopy

175

(6)

Chapter 7. Cluster Analysis

181

(20)

7.1 Introduction

181

(2)

7.2 Distance and Similarity Measures

183

(7)

7.2.1 Euclidean distance

183

(1)

7.2.2 Standardized euclidean distance

183

(1)

7.2.3 Manhattan distance (city block distance)

184

(1)

7.2.4 Distance between clusters and linkage method

185

(4)

7.2.5 Similarity

189

(1)

7.3 Hierarchical Clustering Method

190

(5)

7.4 Nonhierarchical Clustering Method (K-Mean Method)

195

(2)

7.5 Cereal Brand Case Study

197

(4)

Chapter 8. Mahalanobis Distance and Taguchi Method

201

(22)

8.1 Introduction

201

(1)

8.2 Overview of the Mahalanobis-Taguchi System (MTS)

202

(14)

8.2.1 Stage 1: Creation of a baseline Mahalanobis space

203

(2)

8.2.2 Stage 2: Test and analysis of the Mahalanobis measure for abnormal samples

205

(1)

8.2.3 Stage 3 variable screening by using Taguchi orthogonal array experiments

206

(8)

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

214

(2)

8.3 Features of the Mahalanobis-Taguchi System

216

(1)

8.4 The Mahalanobis-Taguchi System Case Study

216

(5)

8.4.1 Clutch disc inspection

217

(4)

8.5 Comments on the Mahalanobis-Taguchi System by Other Researchers and Proposed Alternative Approaches

221

(2)

8.5.1 Alternative approaches

221

(2)

Chapter 9. Path Analysis and the Structural Model

223

(20)

9.1 Introduction

223

(2)

9.2 Path Analysis and the Structural Model

225

(10)

9.2.1 How to use the path diagram and structural model

228

(7)

9.3 Advantages and Disadvantages of Path Analysis and the Structural Model

235

(2)

9.3.1 Advantages

235

(1)

9.3.2 Disadvantages

236

(1)

9.4 Path Analysis Case Studies

237

(6)

9.4.1 Path analysis model relating plastic fuel tank characteristics with its hydrocarbon permeation (Hamade, 1996)

237

(4)

9.4.2 Path analysis of a foundry process (Price and Barth, 1995)

241

(2)

Chapter 10. Multivariate Statistical Process Control

243

(28)

10.1 Introduction

243

(2)

10.2 Multivariate Control Charts for Given Targets

245

(6)

10.2.1 Decomposition of the Hotelling T-2

248

(3)

10.3 Two-Phase T-2 Multivariate Control Charts with Subgroups

251

(8)

10.3.1 Reference sample and new observations

251

(4)

10.3.2 Two-phase T-2 multivariate process control for subgroups

255

(4)

10.4 T2 Control Chart for Individual Observations

259

(6)

10.4.1 Phase I reference sample preparation

260

(4)

10.4.2 Phase II: Process control for new observations

264

(1)

10.5 Principal Component Chart

265

(6)

Appendix Probability Distribution Tables

271

(20)

References

291

(4)

Index

295

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Multivariate Statistical Methods in Quality Management

Summary

Author Biography

Table of Contents

Supplemental Materials