The Mahalanobis-Taguchi Strategy

Preface

Acknowledgments

Terms and Symbols

Definitions of Mathematical and Statistical Terms

1 Introduction

1.1 The Goal

1.2 The Nature of a Multidimensional System

1.3 Multivariate Diagnosis-The State of the Art

1.4 Approach

1.5 Refining the Solution Strategy

1.6 Guide to This Book

2 MTS and MTGS

2.1 A Discussion of Mahalanobis Distance

2.2 Objectives of MTS and MTGS

2.3 Steps in MTS

2.4 Steps in MTGS

2.5 Discussion of Medical Diagnosis Data: Use of MTGS and MTS Methods

2.6 Conclusions

3 Advantages and Limitations of MTS and MTGS

3.1 Direction of Abnormalities

3.2 Example of a Graduate Admission System

3.3 Multicollinearity

3.4 A Discussion of Partial Correlations

3.5 Conclusions

4 Role of Orthogonal Arrays and Signal-to-Noise Ratios in Multivariate Diagnosis

4.1 Role of Orthogonal Arrays

4.2 Role of S/ N Ratios

4.3 Advantages of S/ N ratios

4.4 Conclusions

5 Treatment of Categorical Data in MTS/MTGS Methods

5.1 MTS/ MTGS with Categorical Data

5.2 A Sales and Marketing Application

5.3 Conclusions

6 MTS/ MTGS under a Noise Environment

6.1 MTS/ MTGS with Noise Factors

6.2 Conclusions

7 Determination of Thresholds-A Loss Function Approach

7.1 Why Threshold Is Required in MTS/ MTGS

7.2 Quadratic Loss Function

7.3 QLF for MTS/ MTGS

7.4 Examples

7.5 Conclusions

8 Standard Error of the Measurement Scale

8.1 Why Mahalanobis Distance Is Used for Constructing the Measurement Scale

8.2 Standard Error of the Measurement Scale

8.3 Standard Error for the Medical Diagnosis Example

8.4 Conclusions

9 Advance Topics in Multivariate Diagnosis

9.1 Multivariate Diagnosis Using the Adjoint Matrix Method

9.2 Examples for the Adjoint Matrix Method

9.3 -Adjustment Method for Small Correlations

9.4 Subset Selection Using the Multiple Mahalanobis Distance Method

9.5 Selection of Mahalanobis Space from Historical Data

9.6

GENICHI TAGUCHI, DSc, is Executive Director of the American Supplier Institute and President of Ohken Associates in Japan. Dr. Taguchi, an international authority in quality engineering and robust design, has been awarded the prestigious Deming Prize in 1960 and Willard F. Rockwell Medal in 1986. He was the recipient of the 1995 ASQ's Shewhart medal. In 1998, Dr. Taguchi was elected as an Honorary Member of the ASQ, the ASME, and the Honorary Chairman of the Japanese Quality Engineering Society. He was inducted into the World Level of the Hall of Fame for Engineering, Science, and Technology, USA, in 1998, and the Automotive Hall of Fame, USA, in 1997. In 2000, he was recognized as the Quality Champion of the twentieth century. He authored or coauthored more than 400 technical articles in leading journals and forty books.

RAJESH JUGULUM, Ph.D. is a researcher in the Department of Mechanical Engineering of Massachusetts Institute of Technology. In 2000, he completed his Ph.D. under the guidance of Dr. Genichi Taguchi in Wayne State University. In 1999, he shared ASQ research fellowship grant and in 2000 he received ASQ's Richard A. Freund international scholarship. He was featured as "Face of Quality" in September 2001 issue of Quality Progress. He is the recipient of 2002 ASQ's Feigenbaum medal. He has authored or co-authored several articles in leading technical journals. He is a member of the ASQ and the Japanese Quality Engineering Society and a Fellow of the Royal Statistical Society.