Narayanaswamy Balakrishnan - Accelerated Life Testing of One-shot Devices

1 Cover

2 Title Page Accelerated Life Testing of One‐shot Devices: Data Collection And Analysis Narayanaswamy Balakrishnan McMaster University Hamilton, Canada Man Ho Ling The Education University of Hong Kong Tai Po, Hong Kong Hon Yiu So University of Waterloo Waterloo, Canada

3 Copyright

4 Dedication

5 Preface

6 About the Companion Website

7 Chapter 1: One‐Shot Device Testing Data1.1 Brief Overview 1.2 One‐Shot Devices 1.3 Accelerated Life‐Tests 1.4 Examples in Reliability and Survival Studies 1.5 Recent Developments in One‐Shot Device Testing Analysis

8 Chapter 2: Likelihood Inference2.1 Brief Overview 2.2 Under CSALTs and Different Lifetime Distributions 2.3 EM‐Algorithm 2.4 Interval Estimation 2.5 Simulation Studies 2.6 Case Studies with R Codes

9 Chapter 3: Bayesian Inference3.1 Brief Overview 3.2 Bayesian Framework 3.3 Choice of Priors 3.4 Simulation Studies 3.5 Case Study with R Codes

10 Chapter 4: Model Mis‐Specification Analysis and Model Selection4.1 Brief Overview 4.2 Model Mis‐Specification Analysis 4.3 Model Selection 4.4 Simulation Studies 4.5 Case Study with R Codes

11 Chapter 5: Robust Inference5.1 Brief Overview 5.2 Weighted Minimum Density Power Divergence Estimators 5.3 Asymptotic Distributions 5.4 Robust Wald‐type Tests 5.5 Influence Function 5.6 Simulation Studies 5.7 Case Study with R Codes

12 Chapter 6: Semi‐Parametric Models and Inference6.1 Brief Overview 6.2 Proportional Hazards Models 6.3 Likelihood Inference 6.4 Test of Proportional Hazard Rates 6.5 Simulation Studies 6.6 Case Studies with R Codes

13 Chapter 7: Optimal Design of Tests7.1 Brief Overview 7.2 Optimal Design of CSALTs 7.3 Optimal Design with Budget Constraints 7.4 Case Studies with R Codes 7.5 Sensitivity of Optimal Designs

14 Chapter 8: Design of Simple Step‐Stress Accelerated Life‐Tests8.1 Brief Overview 8.2 One‐Shot Device Testing Data Under Simple SSALTs 8.3 Asymptotic Variance 8.4 Optimal Design of Simple SSALT 8.5 Case Studies with R Codes

15 Chapter 9: Competing‐Risks Models9.1 Brief Overview 9.2 One‐Shot Device Testing Data with Competing Risks 9.3 Likelihood Estimation for Exponential Distribution 9.4 Likelihood Estimation for Weibull Distribution 9.5 Bayesian Estimation 9.6 Simulation Studies 9.7 Case Study with R Codes

16 Chapter 10: One‐Shot Devices with Dependent Components10.1 Brief Overview 10.2 Test Data with Dependent Components 10.3 Copula Models 10.4 Estimation of Dependence 10.5 Simulation Studies 10.6 Case Study with R Codes

17 Chapter 11: Conclusions and Future Directions11.1 Brief Overview 11.2 Concluding Remarks 11.3 Future Directions

18 Appendix A: Derivation of

19 Appendix B: Observed Information Matrix

20 Appendix C: Non‐Identifiable Parameters for SSALTs Under Weibull Distribution

21 Appendix D: Optimal Design Under Weibull Distributions with Fixed

22 Appendix E: Conditional Expectations for Competing Risks Model Under Exponential Distribution

23 Appendix F: Kendall's Tau for Frank Copula

24 Bibliography

25 Author Index

26 Subject Index

27 End User License Agreement

1 Chapter 1 Table 1.1 Failure records on electro‐explosive devices under CSALTs with temp... Table 1.2 Failure records on glass capacitors under CSALTs with two stress fa... Table 1.3 Failure records on solder joints under CSALTs with temperature (K) ... Table 1.4 Failure records on grease‐based magnetorheological fluids under SSA... Table 1.5 The number of mice sacrificed, with tumor from tumorigenecity exper... Table 1.6 The number of mice sacrificed, died without tumor, and died with tu... Table 1.7 Serial sacrifice data on the presence or absence of two disease cat...

2 Chapter 2 Table 2.1 One‐shot device testing data under CSALTs with multiple acceleratin...Table 2.2 The first‐order derivatives of mean lifetime and reliability functi...Table 2.3 CSALTs with two accelerating factors and test groups.Table 2.4 Average numbers of iterations for different sample sizes under the ...Table 2.5 Bias and RMSEs of MLEs of the model parameter, , mean lifetime, a...Table 2.6 Bias and RMSEs of MLEs of the model parameters, mean lifetime, a...Table 2.7 Coverage probabilities and average widths of 95% confidence intervals ...Table 2.8 Coverage probabilities and average widths of 95% asymptotic confidence...Table 2.9 Coverage probabilities and average widths of 95% confidence intervals ...Table 2.10 Coverage probabilities and average widths of 95% confidence intervals...Table 2.11 R codes for defining the data in Tables 1.1 and 1.2.Table 2.12 R codes for point estimation and 95% confidence intervals for the ...Table 2.13 R outputs for inference based on electro‐explosive devices data in...Table 2.14 R outputs for inference based on glass capacitors data in Table 1....

3 Chapter 3Table 3.1 The values of the hyperparameters for Laplace, normal, and beta pri...Table 3.2 Bias and RMSEs of Bayesian estimates of the model parameter, , mean...Table 3.3 Bias and RMSEs of Bayesian estimates of the model parameter, , mean li...Table 3.4 Bias and RMSEs of Bayesian estimates of the model parameter, , mean...Table 3.5 Coverage probabilities (CP) and average widths (AW) of 95% credible...Table 3.6 Coverage probabilities (CP) and average widths (AW) of 95% credible in...Table 3.7 Coverage probabilities (CP) and average widths (AW) of 95% credible...Table 3.8 The values of the hyperparameters for Laplace, normal, and beta pri...Table 3.9 R codes for the estimation of parameters and 95% credible intervals...Table 3.10 Bayesian estimates for glass capacitors data in Table 1.2 for expo...Table 3.11 95% credible intervals for glass capacitors data in Table 1.2 for ...

4 Chapter 4Table 4.1 CSALTs with one stress factor on one‐shot devices for the simulatio...Table 4.2 Relative bias and RMSEs of the estimates of mean lifetime and relia...Table 4.3 Relative bias and RMSEs of the estimates of mean lifetime and relia...Table 4.4 Power of detection of the two distributions by the AIC and distance...Table 4.5 Coverage probability (CP) and average width (AW) of 95% confidence ...Table 4.6 Coverage probability (CP) and average width (AW) of 95% confidence int...Table 4.7 Average width of 95% confidence intervals for mean lifetime and reliab...Table 4.8 Coverage probability of mean lifetime and reliability at four missi...Table 4.9 Modified serial sacrifice data, from Table 1.7, on the presence or ...Table 4.10 R outputs for the log‐likelihood, the AIC and the distance‐based t...