Accelerated Life Testing of One-shot Devices

NARAYANASWAMY BALAKRISHNAN, PhD, is Distinguished University Professor, Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada.MAN HO LING, PhD, is Associate Professor, Department of Mathematics and Information Technology, The Education University of Hong Kong, Hong Kong SAR, China. HON YIU SO is Post-Doctoral Fellow, University of Waterloo, Waterloo, Ontario, Canada.

• Preface xiAbout the Companion Website xiii1 One-Shot Device Testing Data 11.1 Brief Overview 11.2 One-Shot Devices 11.3 Accelerated Life-Tests 31.4 Examples in Reliability and Survival Studies 41.4.1 Electro-Explosive Devices Data 41.4.2 Glass Capacitors Data 51.4.3 Solder Joints Data 51.4.4 Grease-Based Magnetorheological Fluids Data 61.4.5 Mice Tumor Toxicological Data 71.4.6 ED01 Experiment Data 71.4.7 Serial Sacrifice Data 71.5 Recent Developments in One-Shot Device Testing Analysis 102 Likelihood Inference 132.1 Brief Overview 132.2 Under CSALTs and Different Lifetime Distributions 132.3 EM-Algorithm 142.3.1 Exponential Distribution 162.3.2 Gamma Distribution 182.3.3 Weibull Distribution 212.4 Interval Estimation 262.4.1 Asymptotic Confidence Intervals 262.4.2 Approximate Confidence Intervals 282.5 Simulation Studies 302.6 Case Studies with R Codes 413 Bayesian Inference 473.1 Brief Overview 473.2 Bayesian Framework 473.3 Choice of Priors 493.3.1 Laplace Prior 493.3.2 Normal Prior 493.3.3 Beta Prior 503.4 Simulation Studies 513.5 Case Study with R Codes 594 Model Mis-Specification Analysis and Model Selection 654.1 Brief Overview 654.2 Model Mis-Specification Analysis 654.3 Model Selection 664.3.1 Akaike Information Criterion 664.3.2 Bayesian Information Criterion 674.3.3 Distance-Based Test Statistic 684.3.4 Parametric Bootstrap Procedure for Testing Goodness-of-Fit 704.4 Simulation Studies 704.5 Case Study with R Codes 765 Robust Inference 795.1 Brief Overview 795.2 Weighted Minimum Density Power Divergence Estimators 795.3 Asymptotic Distributions 815.4 RobustWald-type Tests 825.5 Influence Function 835.6 Simulation Studies 855.7 Case Study with R Codes 916 Semi-Parametric Models and Inference 956.1 Brief Overview 956.2 Proportional Hazards Models 956.3 Likelihood Inference 976.4 Test of Proportional Hazard Rates 996.5 Simulation Studies 1006.6 Case Studies with R Codes 1027 Optimal Design of Tests 1057.1 Brief Overview 1057.2 Optimal Design of CSALTs 1057.3 Optimal Design with Budget Constraints 1067.3.1 Subject to Specified Budget and Termination Time 1077.3.2 Subject to Standard Deviation and Termination Time 1077.4 Case Studies with R Codes 1087.5 Sensitivity of Optimal Designs 1138 Design of Simple Step-Stress Accelerated Life-Tests 1198.1 Brief Overview 1198.2 One-Shot Device Testing Data Under Simple SSALTs 1198.3 Asymptotic Variance 1218.3.1 Exponential Distribution 1218.3.2 Weibull Distribution 1228.3.3 With a Known Shape Parameter ;;2 1248.3.4 With a Known Parameter About Stress Level ;;1 1258.4 Optimal Design of Simple SSALT 1268.5 Case Studies with R Codes 1288.5.1 SSALT for Exponential Distribution 1288.5.2 SSALT forWeibull Distribution 1319 Competing-Risks Models 1419.1 Brief Overview 1419.2 One-Shot Device Testing Data with Competing Risks 1419.3 Likelihood Estimation for Exponential Distribution 1439.3.1 Without Masked Failure Modes 1449.3.2 With Masked Failure Modes 1479.4 Likelihood Estimation forWeibull Distribution 1499.5 Bayesian Estimation 1559.5.1 Without Masked Failure Modes 1559.5.2 Laplace Prior 1569.5.3 Normal Prior 1579.5.4 Dirichlet Prior 1579.5.5 With Masked Failure Modes 1589.6 Simulation Studies 1599.7 Case Study with R Codes 16510 One-Shot Devices with Dependent Components 17310.1 Brief Overview 17310.2 Test Data with Dependent Components 17310.3 Copula Models 17410.3.1 Family of Archimedean Copulas 17510.3.2 Gumbel–Hougaard Copula 17610.3.3 Frank Copula 17710.4 Estimation of Dependence 18010.5 Simulation Studies 18110.6 Case Study with R Codes 18411 Conclusions and Future Directions 18711.1 Brief Overview 18711.2 Concluding Remarks 18711.2.1 Large Sample Sizes for Flexible Models 18711.2.2 Accurate Estimation 18811.2.3 Good Designs Before Data Analysis 18811.3 Future Directions 18911.3.1 Weibull Lifetime Distribution with Threshold Parameter 18911.3.2 Frailty Models 18911.3.3 Optimal Design of SSALTs with Multiple Stress Levels 18911.3.4 Comparison of CSALTs and SSALTs 190Appendix A Derivation of Hi (a, b) 191Appendix B Observed Information Matrix 193Appendix C Non-Identifiable Parameters for SSALTs Under Weibull Distribution 197Appendix D Optimal Design Under Weibull Distributions with Fixed ;;1 199Appendix E Conditional Expectations for Competing Risks Model Under Exponential Distribution 201Appendix F Kendall’s Tau for Frank Copula 205Bibliography 207Author Index 217Subject Index 221