Cutting-edge measurement technology for multidimensional systems
The Mahalanobis-Taguchi Strategy presents methods for developing multidimensional measurement scales that are up to date with the most current trends in multivariate diagnosis/pattern recognition-namely, using measures and procedures that are data analytic and not dependent upon the distribution of the characteristics defining the system. Applications for these measurement scales are also explored across a wide range of disciplines from manufacturing to medicine.
This book presents methods that integrate mathematical and statistical concepts such as Mahalanobis distance and Gram-Schmidt's orthogonalization method with the principles of Taguchi methods. These completely new systems of measurement and analysis move beyond anything Dr. Taguchi has done in the past. Coverage includes the refined Mahalanobis-Taguchi system, the Mahalanobis-Taguchi-Gram-Schmidt method, the Adjoint Matrix method, and other advanced topics, along with a detailed examination of each method. In addition to examining how real-world problems are solved using these methods, critical comparisons are made between the methods covered here and existing multivariate diagnosis/pattern recognition techniques.
The Mahalanobis-Taguchi Strategy: A Pattern Technology System is an essential book for engineers, designers, and statistical quality experts and programmers in the fields of engineering and computer science, as well as researchers in finance, medicine, statistics, and general science.
Table of contents
Terms and Symbols.
Definitions of Mathematical and Statistical Terms.
1.1 The Goal.
1.2 The Nature of a Multidimensional System.
1.3 Multivariate Diagnosis-The State of the Art.
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.
3 Advantages and Limitations of MTS and MTGS.
3.1 Direction of Abnormalities.
3.2 Example of a Graduate Admission System.
3.4 A Discussion of Partial Correlations.
4 Role of Orthogonal Arrays and Signal-to-Noise Ratios in Multivariate Diagnosis.
4.1 Role of Orthogonal Arrays.
4.2 Role of S/
4.3 Advantages of S/
5 Treatment of Categorical Data in MTS/MTGS Methods.
MTGS with Categorical Data.
5.2 A Sales and Marketing Application.
MTGS under a Noise Environment.
MTGS with Noise Factors.
7 Determination of Thresholds-A Loss Function Approach.
7.1 Why Threshold Is Required in MTS/
7.2 Quadratic Loss Function.
7.3 QLF for MTS/
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.
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.
MTGS versus Other Methods.
10.1 Principal Component Analysis.
10.2 Discrimination and Classification Method.
10.3 Stepwise Regression.
10.4 Test of Additional Information (Rao's Test).
10.5 Multiple Regression Analysis.
10.6 Multivariate Process Control.
10.7 Artificial Neural Networks.
11 Case Studies.
11.1 American Case Studies.
11.2 Japanese Case Studies.
12 Concluding Remarks.
12.1 Important Points of the Proposed Methods.
12.2 Scientific Contributions from MTS/MTGS Methods.
12.3 Limitations of the Proposed Methods.
12.4 Recommendations for Future Research.
A.1 ASI Data Set.
A.2 Principal Component Analysis (MINITAB Output).
A.3 Discriminant and Classification Analysis (MINITAB Output).
A.4 Results of Stepwise Regression (MINITAB Output).
A.5 Multiple Regression Analysis (MINITAB Output).
A.6 Neural Network Analysis (MATLAB Output).
A.7 Variables for Auto Marketing Case Study.