Accelerated testing : statistical models, test plans and data analyses

Accelerated Testing Statistical Models, Test Plans, and Data Analyses......Page 1
Contents......Page 9
Preface......Page 13
1. Introduction and Background......Page 17
1. Survey of Methodology and Applications......Page 19
2. Types of Data......Page 28
3. Types of Acceleration and Stress Loading......Page 31
4. Engineering Considerations......Page 38
5. Common Accelerated Tests......Page 53
6. Statistical Considerations......Page 59
Problems......Page 65
1. Introduction......Page 67
2. Basic Concepts and the Exponential Distribution......Page 69
3. Normal Distribution......Page 74
4. Lognormal Distribution......Page 76
5. Weibull Distribution......Page 79
6. Extreme Value Distribution......Page 81
7. Other Distributions......Page 84
8. Life-Stress Relationships......Page 87
9. Arrhenius Life-Temperature Relationship......Page 91
10. Inverse Power Relationship......Page 101
11. Endurance (Fatigue) Limit Relationships and Distributions......Page 108
12. Other Single Stress Relationships......Page 111
13. Multivariable Relationships......Page 114
14. Spread in Log Life Depends on Stress......Page 121
Problems......Page 123
1. Introduction......Page 129
2. Complete Data and Arrhenius-Lognormal Model......Page 130
3. Complete Data and Power-Weibull Model......Page 144
4. Singly Censored Data......Page 150
5. Multiply Censored Data......Page 155
6. Interval (Read-out) Data......Page 161
Problems......Page 170
1. Introduction......Page 183
2. Least-Squares Methods for Lognormal Life......Page 186
3. Checks on the Linear-Lognormal Model and Data......Page 198
4. Least-Squares Methods for Weibull and Exponential Life......Page 205
5. Checks on the Linear-Weibull Model and Data......Page 219
6. Multivariable Relationships......Page 226
Problems......Page 245
5. Censored Data and Maximum Ukelihood Methods......Page 249
1. Introduction to Maximum Likelihood......Page 250
2. Fit the Simple Model to Right Censored Data......Page 258
3. Assess the Simple Model and Right Censored Data......Page 271
4. Other Models and Types of Data......Page 281
5. Maximum Likelihood Calculations......Page 300
Problems......Page 318
1. Plans for the Simple Model and Complete Data......Page 333
2. Plans for the Simple Model and Singly Censored Data......Page 344
3. Evaluation of a Test Plan by Simulation......Page 365
4. Survey of Test Plans......Page 377
5. ML Theory for Test Plans......Page 380
Problems......Page 387
7. Competing Failure Modes and Size Effect......Page 393
1. Series-System Model......Page 394
2. Series Systems of Identical Parts......Page 399
3. Size Effect......Page 401
4. Nonuniform Stress......Page 403
5. Graphical Analysis......Page 408
6. ML Analysis for Competing Failure Modes......Page 423
7. ML Theory for Competing Modes......Page 429
Problems......Page 433
8. Least-Squares Comparisons for Complete Data......Page 441
1. Hypothesis Tests and Confidence Intervals......Page 442
2. Graphical Comparisons......Page 445
3. Compare Log Standard Deviations......Page 450
4. Compare (Log) Means......Page 453
5. Compare Simple Relationships......Page 457
6. Compare Multivariable Relationships......Page 461
Problems......Page 464
1. Introduction......Page 467
2. One-Sample Comparisons......Page 468
3. Two-Sample Comparisons......Page 474
4. K-Sample Comparisons......Page 481
5. Theory for LR and Related Tests......Page 486
Problems......Page 504
10. Models and Data Analyses for Step and Varying Stress......Page 509
1. Survey of Theory for Tests with Varying Stress......Page 510
2. Step-Stress Model and Data Analyses......Page 511
3. Varying-Stress Model and Data Analyses......Page 522
Problems......Page 529
1. Survey of Applications......Page 537
2. Degradation Models......Page 539
3. Arrhenius Analysis......Page 550
Problems......Page 560
Appendix A. Statistical Tables......Page 565
A1. Standard Normal Cumulative Distribution Function Φ(u)......Page 566
A3. Standard Normal Two-Sided Factors Kp......Page 568
A4. t-Distribution Percentiles t(P;v)......Page 569
A5. Chi-Square Percentiles X2(P;v)......Page 570
A6a. F-Distribution 95% Points F(0.95;v1,v2)......Page 572
A6b. F-Distribution 99% Points F(0.99;v1,v2)......Page 574
A7. Probability Plotting Positions Fi = 10O(i–0.5)/n......Page 576
References......Page 577
Index......Page 595