Accelerated Life Testing of One-shot Devices
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Accelerated Life Testing of One-shot Devices
Data Collection and Analysis
Ling, Man Ho; Balakrishnan, Narayanaswamy; So, Hon Yiu
John Wiley & Sons Inc
04/2021
240
Dura
Inglês
9781119664000
15 a 20 dias
470
Descrição não disponível.
Preface xi
About the Companion Website xiii
1 One-Shot Device Testing Data 1
1.1 Brief Overview 1
1.2 One-Shot Devices 1
1.3 Accelerated Life-Tests 3
1.4 Examples in Reliability and Survival Studies 4
1.4.1 Electro-Explosive Devices Data 4
1.4.2 Glass Capacitors Data 5
1.4.3 Solder Joints Data 5
1.4.4 Grease-Based Magnetorheological Fluids Data 6
1.4.5 Mice Tumor Toxicological Data 7
1.4.6 ED01 Experiment Data 7
1.4.7 Serial Sacrifice Data 7
1.5 Recent Developments in One-Shot Device Testing Analysis 10
2 Likelihood Inference 13
2.1 Brief Overview 13
2.2 Under CSALTs and Different Lifetime Distributions 13
2.3 EM-Algorithm 14
2.3.1 Exponential Distribution 16
2.3.2 Gamma Distribution 18
2.3.3 Weibull Distribution 21
2.4 Interval Estimation 26
2.4.1 Asymptotic Confidence Intervals 26
2.4.2 Approximate Confidence Intervals 28
2.5 Simulation Studies 30
2.6 Case Studies with R Codes 41
3 Bayesian Inference 47
3.1 Brief Overview 47
3.2 Bayesian Framework 47
3.3 Choice of Priors 49
3.3.1 Laplace Prior 49
3.3.2 Normal Prior 49
3.3.3 Beta Prior 50
3.4 Simulation Studies 51
3.5 Case Study with R Codes 59
4 Model Mis-Specification Analysis and Model Selection 65
4.1 Brief Overview 65
4.2 Model Mis-Specification Analysis 65
4.3 Model Selection 66
4.3.1 Akaike Information Criterion 66
4.3.2 Bayesian Information Criterion 67
4.3.3 Distance-Based Test Statistic 68
4.3.4 Parametric Bootstrap Procedure for Testing Goodness-of-Fit 70
4.4 Simulation Studies 70
4.5 Case Study with R Codes 76
5 Robust Inference 79
5.1 Brief Overview 79
5.2 Weighted Minimum Density Power Divergence Estimators 79
5.3 Asymptotic Distributions 81
5.4 RobustWald-type Tests 82
5.5 Influence Function 83
5.6 Simulation Studies 85
5.7 Case Study with R Codes 91
6 Semi-Parametric Models and Inference 95
6.1 Brief Overview 95
6.2 Proportional Hazards Models 95
6.3 Likelihood Inference 97
6.4 Test of Proportional Hazard Rates 99
6.5 Simulation Studies 100
6.6 Case Studies with R Codes 102
7 Optimal Design of Tests 105
7.1 Brief Overview 105
7.2 Optimal Design of CSALTs 105
7.3 Optimal Design with Budget Constraints 106
7.3.1 Subject to Specified Budget and Termination Time 107
7.3.2 Subject to Standard Deviation and Termination Time 107
7.4 Case Studies with R Codes 108
7.5 Sensitivity of Optimal Designs 113
8 Design of Simple Step-Stress Accelerated Life-Tests 119
8.1 Brief Overview 119
8.2 One-Shot Device Testing Data Under Simple SSALTs 119
8.3 Asymptotic Variance 121
8.3.1 Exponential Distribution 121
8.3.2 Weibull Distribution 122
8.3.3 With a Known Shape Parameter 𝑤2 124
8.3.4 With a Known Parameter About Stress Level 𝑤1 125
8.4 Optimal Design of Simple SSALT 126
8.5 Case Studies with R Codes 128
8.5.1 SSALT for Exponential Distribution 128
8.5.2 SSALT forWeibull Distribution 131
9 Competing-Risks Models 141
9.1 Brief Overview 141
9.2 One-Shot Device Testing Data with Competing Risks 141
9.3 Likelihood Estimation for Exponential Distribution 143
9.3.1 Without Masked Failure Modes 144
9.3.2 With Masked Failure Modes 147
9.4 Likelihood Estimation forWeibull Distribution 149
9.5 Bayesian Estimation 155
9.5.1 Without Masked Failure Modes 155
9.5.2 Laplace Prior 156
9.5.3 Normal Prior 157
9.5.4 Dirichlet Prior 157
9.5.5 With Masked Failure Modes 158
9.6 Simulation Studies 159
9.7 Case Study with R Codes 165
10 One-Shot Devices with Dependent Components 173
10.1 Brief Overview 173
10.2 Test Data with Dependent Components 173
10.3 Copula Models 174
10.3.1 Family of Archimedean Copulas 175
10.3.2 Gumbel-Hougaard Copula 176
10.3.3 Frank Copula 177
10.4 Estimation of Dependence 180
10.5 Simulation Studies 181
10.6 Case Study with R Codes 184
11 Conclusions and Future Directions 187
11.1 Brief Overview 187
11.2 Concluding Remarks 187
11.2.1 Large Sample Sizes for Flexible Models 187
11.2.2 Accurate Estimation 188
11.2.3 Good Designs Before Data Analysis 188
11.3 Future Directions 189
11.3.1 Weibull Lifetime Distribution with Threshold Parameter 189
11.3.2 Frailty Models 189
11.3.3 Optimal Design of SSALTs with Multiple Stress Levels 189
11.3.4 Comparison of CSALTs and SSALTs 190
Appendix A Derivation of Hi (a, b) 191
Appendix B Observed Information Matrix 193
Appendix C Non-Identifiable Parameters for SSALTs Under Weibull Distribution 197
Appendix D Optimal Design Under Weibull Distributions with Fixed 𝒘1 199
Appendix E Conditional Expectations for Competing Risks Model Under Exponential Distribution 201
Appendix F Kendall's Tau for Frank Copula 205
Bibliography 207
Author Index 217
Subject Index 221
About the Companion Website xiii
1 One-Shot Device Testing Data 1
1.1 Brief Overview 1
1.2 One-Shot Devices 1
1.3 Accelerated Life-Tests 3
1.4 Examples in Reliability and Survival Studies 4
1.4.1 Electro-Explosive Devices Data 4
1.4.2 Glass Capacitors Data 5
1.4.3 Solder Joints Data 5
1.4.4 Grease-Based Magnetorheological Fluids Data 6
1.4.5 Mice Tumor Toxicological Data 7
1.4.6 ED01 Experiment Data 7
1.4.7 Serial Sacrifice Data 7
1.5 Recent Developments in One-Shot Device Testing Analysis 10
2 Likelihood Inference 13
2.1 Brief Overview 13
2.2 Under CSALTs and Different Lifetime Distributions 13
2.3 EM-Algorithm 14
2.3.1 Exponential Distribution 16
2.3.2 Gamma Distribution 18
2.3.3 Weibull Distribution 21
2.4 Interval Estimation 26
2.4.1 Asymptotic Confidence Intervals 26
2.4.2 Approximate Confidence Intervals 28
2.5 Simulation Studies 30
2.6 Case Studies with R Codes 41
3 Bayesian Inference 47
3.1 Brief Overview 47
3.2 Bayesian Framework 47
3.3 Choice of Priors 49
3.3.1 Laplace Prior 49
3.3.2 Normal Prior 49
3.3.3 Beta Prior 50
3.4 Simulation Studies 51
3.5 Case Study with R Codes 59
4 Model Mis-Specification Analysis and Model Selection 65
4.1 Brief Overview 65
4.2 Model Mis-Specification Analysis 65
4.3 Model Selection 66
4.3.1 Akaike Information Criterion 66
4.3.2 Bayesian Information Criterion 67
4.3.3 Distance-Based Test Statistic 68
4.3.4 Parametric Bootstrap Procedure for Testing Goodness-of-Fit 70
4.4 Simulation Studies 70
4.5 Case Study with R Codes 76
5 Robust Inference 79
5.1 Brief Overview 79
5.2 Weighted Minimum Density Power Divergence Estimators 79
5.3 Asymptotic Distributions 81
5.4 RobustWald-type Tests 82
5.5 Influence Function 83
5.6 Simulation Studies 85
5.7 Case Study with R Codes 91
6 Semi-Parametric Models and Inference 95
6.1 Brief Overview 95
6.2 Proportional Hazards Models 95
6.3 Likelihood Inference 97
6.4 Test of Proportional Hazard Rates 99
6.5 Simulation Studies 100
6.6 Case Studies with R Codes 102
7 Optimal Design of Tests 105
7.1 Brief Overview 105
7.2 Optimal Design of CSALTs 105
7.3 Optimal Design with Budget Constraints 106
7.3.1 Subject to Specified Budget and Termination Time 107
7.3.2 Subject to Standard Deviation and Termination Time 107
7.4 Case Studies with R Codes 108
7.5 Sensitivity of Optimal Designs 113
8 Design of Simple Step-Stress Accelerated Life-Tests 119
8.1 Brief Overview 119
8.2 One-Shot Device Testing Data Under Simple SSALTs 119
8.3 Asymptotic Variance 121
8.3.1 Exponential Distribution 121
8.3.2 Weibull Distribution 122
8.3.3 With a Known Shape Parameter 𝑤2 124
8.3.4 With a Known Parameter About Stress Level 𝑤1 125
8.4 Optimal Design of Simple SSALT 126
8.5 Case Studies with R Codes 128
8.5.1 SSALT for Exponential Distribution 128
8.5.2 SSALT forWeibull Distribution 131
9 Competing-Risks Models 141
9.1 Brief Overview 141
9.2 One-Shot Device Testing Data with Competing Risks 141
9.3 Likelihood Estimation for Exponential Distribution 143
9.3.1 Without Masked Failure Modes 144
9.3.2 With Masked Failure Modes 147
9.4 Likelihood Estimation forWeibull Distribution 149
9.5 Bayesian Estimation 155
9.5.1 Without Masked Failure Modes 155
9.5.2 Laplace Prior 156
9.5.3 Normal Prior 157
9.5.4 Dirichlet Prior 157
9.5.5 With Masked Failure Modes 158
9.6 Simulation Studies 159
9.7 Case Study with R Codes 165
10 One-Shot Devices with Dependent Components 173
10.1 Brief Overview 173
10.2 Test Data with Dependent Components 173
10.3 Copula Models 174
10.3.1 Family of Archimedean Copulas 175
10.3.2 Gumbel-Hougaard Copula 176
10.3.3 Frank Copula 177
10.4 Estimation of Dependence 180
10.5 Simulation Studies 181
10.6 Case Study with R Codes 184
11 Conclusions and Future Directions 187
11.1 Brief Overview 187
11.2 Concluding Remarks 187
11.2.1 Large Sample Sizes for Flexible Models 187
11.2.2 Accurate Estimation 188
11.2.3 Good Designs Before Data Analysis 188
11.3 Future Directions 189
11.3.1 Weibull Lifetime Distribution with Threshold Parameter 189
11.3.2 Frailty Models 189
11.3.3 Optimal Design of SSALTs with Multiple Stress Levels 189
11.3.4 Comparison of CSALTs and SSALTs 190
Appendix A Derivation of Hi (a, b) 191
Appendix B Observed Information Matrix 193
Appendix C Non-Identifiable Parameters for SSALTs Under Weibull Distribution 197
Appendix D Optimal Design Under Weibull Distributions with Fixed 𝒘1 199
Appendix E Conditional Expectations for Competing Risks Model Under Exponential Distribution 201
Appendix F Kendall's Tau for Frank Copula 205
Bibliography 207
Author Index 217
Subject Index 221
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
<p>one-shot device testing; one-shot device data; one-shot device analysis; one-shot device life-test;one-shot device statistical modeling; one-shot device inferential methods; one-shot device statistical techniques; one-shot device reliability; one-shot device optimal designs</p>
Preface xi
About the Companion Website xiii
1 One-Shot Device Testing Data 1
1.1 Brief Overview 1
1.2 One-Shot Devices 1
1.3 Accelerated Life-Tests 3
1.4 Examples in Reliability and Survival Studies 4
1.4.1 Electro-Explosive Devices Data 4
1.4.2 Glass Capacitors Data 5
1.4.3 Solder Joints Data 5
1.4.4 Grease-Based Magnetorheological Fluids Data 6
1.4.5 Mice Tumor Toxicological Data 7
1.4.6 ED01 Experiment Data 7
1.4.7 Serial Sacrifice Data 7
1.5 Recent Developments in One-Shot Device Testing Analysis 10
2 Likelihood Inference 13
2.1 Brief Overview 13
2.2 Under CSALTs and Different Lifetime Distributions 13
2.3 EM-Algorithm 14
2.3.1 Exponential Distribution 16
2.3.2 Gamma Distribution 18
2.3.3 Weibull Distribution 21
2.4 Interval Estimation 26
2.4.1 Asymptotic Confidence Intervals 26
2.4.2 Approximate Confidence Intervals 28
2.5 Simulation Studies 30
2.6 Case Studies with R Codes 41
3 Bayesian Inference 47
3.1 Brief Overview 47
3.2 Bayesian Framework 47
3.3 Choice of Priors 49
3.3.1 Laplace Prior 49
3.3.2 Normal Prior 49
3.3.3 Beta Prior 50
3.4 Simulation Studies 51
3.5 Case Study with R Codes 59
4 Model Mis-Specification Analysis and Model Selection 65
4.1 Brief Overview 65
4.2 Model Mis-Specification Analysis 65
4.3 Model Selection 66
4.3.1 Akaike Information Criterion 66
4.3.2 Bayesian Information Criterion 67
4.3.3 Distance-Based Test Statistic 68
4.3.4 Parametric Bootstrap Procedure for Testing Goodness-of-Fit 70
4.4 Simulation Studies 70
4.5 Case Study with R Codes 76
5 Robust Inference 79
5.1 Brief Overview 79
5.2 Weighted Minimum Density Power Divergence Estimators 79
5.3 Asymptotic Distributions 81
5.4 RobustWald-type Tests 82
5.5 Influence Function 83
5.6 Simulation Studies 85
5.7 Case Study with R Codes 91
6 Semi-Parametric Models and Inference 95
6.1 Brief Overview 95
6.2 Proportional Hazards Models 95
6.3 Likelihood Inference 97
6.4 Test of Proportional Hazard Rates 99
6.5 Simulation Studies 100
6.6 Case Studies with R Codes 102
7 Optimal Design of Tests 105
7.1 Brief Overview 105
7.2 Optimal Design of CSALTs 105
7.3 Optimal Design with Budget Constraints 106
7.3.1 Subject to Specified Budget and Termination Time 107
7.3.2 Subject to Standard Deviation and Termination Time 107
7.4 Case Studies with R Codes 108
7.5 Sensitivity of Optimal Designs 113
8 Design of Simple Step-Stress Accelerated Life-Tests 119
8.1 Brief Overview 119
8.2 One-Shot Device Testing Data Under Simple SSALTs 119
8.3 Asymptotic Variance 121
8.3.1 Exponential Distribution 121
8.3.2 Weibull Distribution 122
8.3.3 With a Known Shape Parameter 𝑤2 124
8.3.4 With a Known Parameter About Stress Level 𝑤1 125
8.4 Optimal Design of Simple SSALT 126
8.5 Case Studies with R Codes 128
8.5.1 SSALT for Exponential Distribution 128
8.5.2 SSALT forWeibull Distribution 131
9 Competing-Risks Models 141
9.1 Brief Overview 141
9.2 One-Shot Device Testing Data with Competing Risks 141
9.3 Likelihood Estimation for Exponential Distribution 143
9.3.1 Without Masked Failure Modes 144
9.3.2 With Masked Failure Modes 147
9.4 Likelihood Estimation forWeibull Distribution 149
9.5 Bayesian Estimation 155
9.5.1 Without Masked Failure Modes 155
9.5.2 Laplace Prior 156
9.5.3 Normal Prior 157
9.5.4 Dirichlet Prior 157
9.5.5 With Masked Failure Modes 158
9.6 Simulation Studies 159
9.7 Case Study with R Codes 165
10 One-Shot Devices with Dependent Components 173
10.1 Brief Overview 173
10.2 Test Data with Dependent Components 173
10.3 Copula Models 174
10.3.1 Family of Archimedean Copulas 175
10.3.2 Gumbel-Hougaard Copula 176
10.3.3 Frank Copula 177
10.4 Estimation of Dependence 180
10.5 Simulation Studies 181
10.6 Case Study with R Codes 184
11 Conclusions and Future Directions 187
11.1 Brief Overview 187
11.2 Concluding Remarks 187
11.2.1 Large Sample Sizes for Flexible Models 187
11.2.2 Accurate Estimation 188
11.2.3 Good Designs Before Data Analysis 188
11.3 Future Directions 189
11.3.1 Weibull Lifetime Distribution with Threshold Parameter 189
11.3.2 Frailty Models 189
11.3.3 Optimal Design of SSALTs with Multiple Stress Levels 189
11.3.4 Comparison of CSALTs and SSALTs 190
Appendix A Derivation of Hi (a, b) 191
Appendix B Observed Information Matrix 193
Appendix C Non-Identifiable Parameters for SSALTs Under Weibull Distribution 197
Appendix D Optimal Design Under Weibull Distributions with Fixed 𝒘1 199
Appendix E Conditional Expectations for Competing Risks Model Under Exponential Distribution 201
Appendix F Kendall's Tau for Frank Copula 205
Bibliography 207
Author Index 217
Subject Index 221
About the Companion Website xiii
1 One-Shot Device Testing Data 1
1.1 Brief Overview 1
1.2 One-Shot Devices 1
1.3 Accelerated Life-Tests 3
1.4 Examples in Reliability and Survival Studies 4
1.4.1 Electro-Explosive Devices Data 4
1.4.2 Glass Capacitors Data 5
1.4.3 Solder Joints Data 5
1.4.4 Grease-Based Magnetorheological Fluids Data 6
1.4.5 Mice Tumor Toxicological Data 7
1.4.6 ED01 Experiment Data 7
1.4.7 Serial Sacrifice Data 7
1.5 Recent Developments in One-Shot Device Testing Analysis 10
2 Likelihood Inference 13
2.1 Brief Overview 13
2.2 Under CSALTs and Different Lifetime Distributions 13
2.3 EM-Algorithm 14
2.3.1 Exponential Distribution 16
2.3.2 Gamma Distribution 18
2.3.3 Weibull Distribution 21
2.4 Interval Estimation 26
2.4.1 Asymptotic Confidence Intervals 26
2.4.2 Approximate Confidence Intervals 28
2.5 Simulation Studies 30
2.6 Case Studies with R Codes 41
3 Bayesian Inference 47
3.1 Brief Overview 47
3.2 Bayesian Framework 47
3.3 Choice of Priors 49
3.3.1 Laplace Prior 49
3.3.2 Normal Prior 49
3.3.3 Beta Prior 50
3.4 Simulation Studies 51
3.5 Case Study with R Codes 59
4 Model Mis-Specification Analysis and Model Selection 65
4.1 Brief Overview 65
4.2 Model Mis-Specification Analysis 65
4.3 Model Selection 66
4.3.1 Akaike Information Criterion 66
4.3.2 Bayesian Information Criterion 67
4.3.3 Distance-Based Test Statistic 68
4.3.4 Parametric Bootstrap Procedure for Testing Goodness-of-Fit 70
4.4 Simulation Studies 70
4.5 Case Study with R Codes 76
5 Robust Inference 79
5.1 Brief Overview 79
5.2 Weighted Minimum Density Power Divergence Estimators 79
5.3 Asymptotic Distributions 81
5.4 RobustWald-type Tests 82
5.5 Influence Function 83
5.6 Simulation Studies 85
5.7 Case Study with R Codes 91
6 Semi-Parametric Models and Inference 95
6.1 Brief Overview 95
6.2 Proportional Hazards Models 95
6.3 Likelihood Inference 97
6.4 Test of Proportional Hazard Rates 99
6.5 Simulation Studies 100
6.6 Case Studies with R Codes 102
7 Optimal Design of Tests 105
7.1 Brief Overview 105
7.2 Optimal Design of CSALTs 105
7.3 Optimal Design with Budget Constraints 106
7.3.1 Subject to Specified Budget and Termination Time 107
7.3.2 Subject to Standard Deviation and Termination Time 107
7.4 Case Studies with R Codes 108
7.5 Sensitivity of Optimal Designs 113
8 Design of Simple Step-Stress Accelerated Life-Tests 119
8.1 Brief Overview 119
8.2 One-Shot Device Testing Data Under Simple SSALTs 119
8.3 Asymptotic Variance 121
8.3.1 Exponential Distribution 121
8.3.2 Weibull Distribution 122
8.3.3 With a Known Shape Parameter 𝑤2 124
8.3.4 With a Known Parameter About Stress Level 𝑤1 125
8.4 Optimal Design of Simple SSALT 126
8.5 Case Studies with R Codes 128
8.5.1 SSALT for Exponential Distribution 128
8.5.2 SSALT forWeibull Distribution 131
9 Competing-Risks Models 141
9.1 Brief Overview 141
9.2 One-Shot Device Testing Data with Competing Risks 141
9.3 Likelihood Estimation for Exponential Distribution 143
9.3.1 Without Masked Failure Modes 144
9.3.2 With Masked Failure Modes 147
9.4 Likelihood Estimation forWeibull Distribution 149
9.5 Bayesian Estimation 155
9.5.1 Without Masked Failure Modes 155
9.5.2 Laplace Prior 156
9.5.3 Normal Prior 157
9.5.4 Dirichlet Prior 157
9.5.5 With Masked Failure Modes 158
9.6 Simulation Studies 159
9.7 Case Study with R Codes 165
10 One-Shot Devices with Dependent Components 173
10.1 Brief Overview 173
10.2 Test Data with Dependent Components 173
10.3 Copula Models 174
10.3.1 Family of Archimedean Copulas 175
10.3.2 Gumbel-Hougaard Copula 176
10.3.3 Frank Copula 177
10.4 Estimation of Dependence 180
10.5 Simulation Studies 181
10.6 Case Study with R Codes 184
11 Conclusions and Future Directions 187
11.1 Brief Overview 187
11.2 Concluding Remarks 187
11.2.1 Large Sample Sizes for Flexible Models 187
11.2.2 Accurate Estimation 188
11.2.3 Good Designs Before Data Analysis 188
11.3 Future Directions 189
11.3.1 Weibull Lifetime Distribution with Threshold Parameter 189
11.3.2 Frailty Models 189
11.3.3 Optimal Design of SSALTs with Multiple Stress Levels 189
11.3.4 Comparison of CSALTs and SSALTs 190
Appendix A Derivation of Hi (a, b) 191
Appendix B Observed Information Matrix 193
Appendix C Non-Identifiable Parameters for SSALTs Under Weibull Distribution 197
Appendix D Optimal Design Under Weibull Distributions with Fixed 𝒘1 199
Appendix E Conditional Expectations for Competing Risks Model Under Exponential Distribution 201
Appendix F Kendall's Tau for Frank Copula 205
Bibliography 207
Author Index 217
Subject Index 221
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
