The Mahalanobis-Taguchi Strategy: A Pattern Technology System

• Autore: Taguchi Gen'ichi <1924-2012>
• Pubblicazione: [Place of publication not identified], : Wiley Imprint, 2002
• Descrizione fisica: 1 online resource (xxii, 234 pages) : illustrations
• Disciplina: 658.5/62
• Soggetto topico: Pattern recognition systems
• Persona (resp. second.): JugulumRajesh
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references (pages [207]-212) and index.
• Nota di contenuto: 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. -- 1.2.1 Description of Multidimensional Systems. -- 1.2.2 Correlations between the Variables. -- 1.2.3 Mahalanobis Distance. -- 1.2.4 Robust Engineering/ Taguchi Methods. -- 1.3 Multivariate Diagnosis The State of the Art. -- 1.3.1 Principal Component Analysis. -- 1.3.2 Discrimination and Classification Method. -- 1.3.3 Stepwise Regression. -- 1.3.4 Test of Additional Information (Rao s Test). -- 1.3.5 Multiple Regression. -- 1.3.6 Multivariate Process Control Charts. -- 1.3.7 Artificial Neural Networks. -- 1.4 Approach. -- 1.4.1 Classification versus Measurement. -- 1.4.2 Normals versus Abnormals. -- 1.4.3 Probabilistic versus Data Analytic. -- 1.4.4 Dimensionality Reduction. -- 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. -- 2.2.1 Mahalanobis Distance (Inverse Matrix Method). -- 2.2.2 Gram Schmidt Orthogonalization Process. -- 2.2.3 Proof That Equations 2.2 and 2.3 Are the Same. -- 2.2.4 Calculation of the Mean of the Mahalanobis Space. -- 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. -- 3.1.1 The Gram Schmidt Process. -- 3.1.2 Identification of the Direction of Abnormals. -- 3.1.3 Decision Rule for Higher Dimensions. -- 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. -- 4.3.1 S/ N Ratio as a Simple Measure to Identify Useful Variables. -- 4.3.2 S/ N Ratio as a Measure of Functionality of the System. -- 4.3.3 S/ N Ratio to Predict the Given Conditions. -- 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. -- 5.2.1 Selection of Suitable Variables. -- 5.2.2 Description of the Variables. -- 5.2.3 Construction of Mahalanobis Space. -- 5.2.4 Validation of the Measurement Scale. -- 5.2.5 Identification of Useful Variables (Developing Stage). -- 5.2.6 S/ N Ratio of the System (Before and After). -- 5.3 Conclusions. -- 6 MTS/ MTGS under a Noise Environment. -- 6.1 MTS/ MTGS with Noise Factors. -- 6.1.1 Treat Each Level of the Noise Factor Separately. -- 6.1.2 Include the Noise Factor as One of the Variables. -- 6.1.3 Combine Variables of Different Levels of the Noise Factor. -- 6.1.4 Do Not Consider the Noise Factor If It Cannot Be Measured. -- 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. -- 7.2.1 QLF for the Nominal-the-Best Characteristic. -- 7.2.2 QLF for the Larger-the-Better Characteristic. -- 7.2.3 QLF for the Smaller-the-Better Characteristic. -- 7.3 QLF for MTS/ MTGS. -- 7.3.1 Determination of Threshold. -- 7.3.2 When Only Good Abnormals Are Present. -- 7.4 Examples. -- 7.4.1 Medical Diagnosis Case. -- 7.4.2 A Student Admission System. -- 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. -- 9.1.1 Related Topics of Matrix Theory. -- 9.1.2 Adjoint Matrix Method for Handling Multicollinearity. -- 9.2 Examples for the Adjoint Matrix Method. -- 9.2.1 Example 1. -- 9.2.2 Example 2. -- 9.3 β-Adjustment Method for Small Correlations. -- 9.4 Subset Selection Using the Multiple Mahalanobis Distance Method. -- 9.4.1 Steps in the MMD Method. -- 9.4.2 Example. -- 9.5 Selection of Mahalanobis Space from Historical Data. -- 9.6 Conclusions. -- 10 MTS/ MTGS versus Other Methods. -- 10.1 Principal Component Analysis. -- 10.2 Discrimination and Classification Method. -- 10.2.1 Fisher s Discriminant Function. -- 10.2.2 Use of Mahalanobis Distance. -- 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. -- 10.7.1 Feed-Forward (Backpropagation) Method. -- 10.7.2 Theoretical Comparison. -- 10.7.3 Medical Diagnosis Data Analysis. -- 10.8 Conclusions. -- 11 Case Studies. -- 11.1 American Case Studies. -- 11.1.1 Auto Marketing Case Study. -- 11.1.2 Gear-Motor Assembly Case Study. -- 11.1.3 ASQ Research Fellowship Grant Case Study. -- 11.1.4 Improving the Transmission Inspection System Using MTS. -- 11.2 Japanese Case Studies. -- 11.2.1 Improvement of the Utility Rate of Nitrogen While Brewing Soy Sauce. -- 11.2.2 Application of MTS for Measuring Oil in Water Emulsion. -- 11.2.3 Prediction of Fasting Plasma Glucose (FPG) from Repetitive Annual Health Checkup Data. -- 11.3 Conclusions. -- 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. -- Bibliography. -- Appendixes. -- 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. -- Index.
• Sommario/riassunto: Cuttingedge measurement technology for multidimensional systems The MahalanobisTaguchi Strategy presents methods for developing multidimensional measurement scales that are up to date with the most current trends in multivariate diagnosis/pattern recognitionnamely, 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 GramSchmidts 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 MahalanobisTaguchi system, the MahalanobisTaguchiGramSchmidt method, the Adjoint Matrix method, and other advanced topics, along with a detailed examination of each method. In addition to examining how realworld problems are solved using these methods, critical comparisons are made between the methods covered here and existing multivariate diagnosis/pattern recognition techniques. The MahalanobisTaguchi 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.
• Titolo autorizzato: The Mahalanobis-Taguchi Strategy: A Pattern Technology System
• ISBN: 0-471-27533-6; 0-470-17224-X; 0-470-34606-X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910678111303321
• Lo trovi qui: Univ. Federico II