Living without Mathematical Statistics. Accurate Analysis, Diagnosis and Prognosis based on the Taguchi Method

Preface......Page 3
Contents......Page 5
1.1 History......Page 9
1.2 Beginning......Page 11
--- Analysis of Variables......Page 13
Abstract......Page 14
2.1 Concept and Usefulness of the Signal-to-Noise Ratio......Page 15
2.2 Static Systems......Page 21
2.3 Dynamic Systems......Page 25
2.4 Relative Signal Values......Page 29
2.5 Orthogonal Arrays and Their Design......Page 33
2.6 Types of Orthogonal Arrays......Page 38
2.7 Modification of Orthogonal Arrays......Page 40
2.8 Interpretation of Orthogonal Arrays......Page 42
2.9 Percentage of Effect Contribution......Page 48
2.10 Scope of Validity of a Model Prediction......Page 49
2.11 Nonlinear Transfer Functions of Variables......Page 51
2.12 Interaction with Noise Factors......Page 53
2.13 Neutralizations of Noise Factors......Page 54
3.1 Classification of Systems......Page 60
3.3 Systems with Continuous Data Input and Digital Data Output......Page 61
3.4 Systems with Digital Data Input and Continuous Data Output......Page 63
3.5 Systems with Digital Data......Page 64
3.6.1 Comparison of Two Sorting Machines......Page 70
3.6.2 Magnetic Separator......Page 72
3.6.3 Satellite Receiver......Page 74
3.7 Functional Range with Two Signal-to-Noise Key Figures......Page 77
3.8 Ideal Function......Page 80
Abstract......Page 84
4.1 Macroscopic Description......Page 85
4.2 Signal-to-Noise Ratios in Reaction Kinetics......Page 87
4.2.1 Irreversible Chemical Reaction of First Order......Page 88
4.2.2 Irreversible Chemical Reaction of Second Order......Page 90
4.2.3 Reversible Chemical Reaction of First Order......Page 91
4.2.4 Parallel Reaction of First Order......Page 92
4.2.5 Consecutive Reaction of First Order......Page 93
4.2.6 Double Consecutive Reaction of First Order......Page 96
4.3 Optimization Procedures for Time-Dependent Systems......Page 98
4.4 Continuously Running Processes......Page 100
4.5 Systems with Complex Signal-to-Noise Ratios......Page 103
4.6 Systems with More Than One Signal Factor......Page 107
Abstract......Page 116
5.1 Standardized Signal-to-Noise Key Figure and Terms of Higher Order......Page 117
5.2 Analyses of a Nonlinear System......Page 127
5.3 Incomplete Data—Sequential Iteration......Page 131
5.4 Loss Function......Page 134
5.5 Tolerances in Static Systems......Page 137
5.6 Tolerances in Dynamic Systems......Page 146
5.8 Tolerances for Coupled Parameters......Page 149
5.9 Safety Factor......Page 151
6.1 Identification of Defective Components......Page 155
6.2 Mixtures/Solutions from Several Components......Page 156
6.3 Testing of Hardware and Software......Page 159
6.4 Dealing with Qualitative Characteristics......Page 161
6.5 Quantitative Modelling......Page 165
6.6.1 Durability Test of Two Materials......Page 172
6.6.2 Evaluation of a Medicative Therapy......Page 174
--- Pattern Recognition & Diagnosis......Page 177
7.1 Correlated Variables......Page 178
7.2 The Mahalanobis Algorithm......Page 182
7.4 Effectiveness of Variables......Page 190
7.5 Parameter Screening with Static Signal-to-Noise Indices......Page 197
7.6 Parameter Screening with Dynamic Signal-to-Noise Indices......Page 213
7.7 Root-Cause-Analyses......Page 217
7.8 Directional Recognition......Page 221
8.1 Procedure of Orthogonalization According to Gram–Schmidt......Page 231
8.2 Parameter Screening of Orthogonalized Variables with Orthogonal Array......Page 234
8.3 Parameter Screening of Orthogonalized Variables Without Orthogonal Array......Page 238
8.4 Root-Cause-Analysis with Orthogonalized Variables......Page 243
8.5 Procedure with the Adjoint Correlation Matrix......Page 244
8.6 Mahalanobis Distance with the Adjoint Matrix......Page 246
8.7 Clinical Case Study Revisited: Application of the Adjoint Correlation Matrix......Page 248
8.8 Parameter Screening and Root-Cause-Analysis......Page 250
9.1 Adjustments to the Threshold Value......Page 253
9.3 Multiple Mahalanobis Distance......Page 255
9.4 Clinical Case Study Revisited: Application of Squared Multiple Mahalanobis Distance......Page 257
9.5 Evaluations of Therapies......Page 261
9.6 Data Discrimination Without Unit Group......Page 264
9.7 Scope of the Mathematical Procedures and the Re-normalization......Page 269
9.8 Dealing with Categorical Data......Page 271
10.1 Structured Approach......Page 273
10.2 Pattern Recognition......Page 274
10.3 Alarm Systems......Page 277
10.4 Driving Assistants......Page 278
10.5 Monitoring of Patients......Page 279
10.6 Original and Fake......Page 280
10.7 Proposal for Research Project in the Field of Biology......Page 281
10.9 Proposal for Research Project in the Field of Astronomy......Page 282
--- Prognoses......Page 284
Abstract......Page 285
11.1 Issues in Retrospect......Page 286
11.2 Prognosis Algorithms with Linear Equation......Page 295
11.3 Selecting a Zero Point......Page 305
11.4 Size of the Reference Group......Page 308
11.5 Transformation of Data......Page 311
11.6 Prognosis Algorithm with Squared Mahalanobis Distance......Page 318
11.7 Size of the Reference Group......Page 324
11.9 Procedure Applying the Adjoint Correlation Matrix......Page 327
11.10 Combined Procedures......Page 328
11.11 Variables Without Deviation......Page 338
Abstract......Page 340
12.2 Screening with Linear Equation......Page 341
12.3 Screening with Quadratic Equation......Page 344
12.4 Screening with Quadratic Equation Without Correlation Matrix......Page 352
12.5 Procedure Selection......Page 357
12.6 Prognosis Algorithm Without Numerical Key Figures......Page 362
12.7 Procedure with One-Step Reduction of Variables......Page 363
12.8 Procedure with Multiple Reduction of Variables......Page 366
12.9 Prediction and Modeling......Page 370
12.10 Properties of the Algorithms for Prognosis......Page 374
Epilogue......Page 375
Appendix A......Page 376
Appendix B......Page 415
Refs......Page 495
Index......Page 502