Accelerated Life Testing of One-shot Devices

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Narayanaswamy Balakrishnan. Accelerated Life Testing of One-shot Devices

Table of Contents

List of Tables

List of Illustrations

Guide

Pages

Accelerated Life Testing of One‐shot Devices:

Preface

About the Companion Website

1 One‐Shot Device Testing Data. 1.1 Brief Overview

1.2 One‐Shot Devices

1.3 Accelerated Life‐Tests

1.4 Examples in Reliability and Survival Studies. 1.4.1 Electro‐Explosive Devices Data

1.4.2 Glass Capacitors Data

1.4.3 Solder Joints Data

1.4.4 Grease‐Based Magnetorheological Fluids Data

1.4.5 Mice Tumor Toxicological Data

1.4.6 ED01 Experiment Data

1.4.7 Serial Sacrifice Data

1.5 Recent Developments in One‐Shot Device Testing Analysis

2 Likelihood Inference. 2.1 Brief Overview

2.2 Under CSALTs and Different Lifetime Distributions

2.3 EM‐Algorithm

2.3.1 Exponential Distribution

2.3.2 Gamma Distribution

2.3.3 Weibull Distribution

2.4 Interval Estimation

2.4.1 Asymptotic Confidence Intervals

2.4.2 Approximate Confidence Intervals

2.5 Simulation Studies

2.6 Case Studies with R Codes

3 Bayesian Inference. 3.1 Brief Overview

3.2 Bayesian Framework

3.3 Choice of Priors

3.3.1 Laplace Prior

3.3.2 Normal Prior

3.3.3 Beta Prior

3.4 Simulation Studies

3.5 Case Study with R Codes

4 Model Mis‐Specification Analysis and Model Selection. 4.1 Brief Overview

4.2 Model Mis‐Specification Analysis

4.3 Model Selection

4.3.1 Akaike Information Criterion

4.3.2 Bayesian Information Criterion

4.3.3 Distance‐Based Test Statistic

4.3.4 Parametric Bootstrap Procedure for Testing Goodness‐of‐Fit

4.4 Simulation Studies

4.5 Case Study with R Codes

5 Robust Inference. 5.1 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

6 Semi‐Parametric Models and Inference. 6.1 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

7 Optimal Design of Tests. 7.1 Brief Overview

7.2 Optimal Design of CSALTs

7.3 Optimal Design with Budget Constraints

7.3.1 Subject to Specified Budget and Termination Time

7.3.2 Subject to Standard Deviation and Termination Time

7.4 Case Studies with R Codes

7.5 Sensitivity of Optimal Designs

8 Design of Simple Step‐Stress Accelerated Life‐Tests. 8.1 Brief Overview

8.2 One‐Shot Device Testing Data Under Simple SSALTs

8.3 Asymptotic Variance. 8.3.1 Exponential Distribution

8.3.2 Weibull Distribution

8.3.3 With a Known Shape Parameter

8.3.4 With a Known Parameter About Stress Level

8.4 Optimal Design of Simple SSALT

8.5 Case Studies with R Codes. 8.5.1 SSALT for Exponential Distribution

8.5.2 SSALT for Weibull Distribution

9 Competing‐Risks Models. 9.1 Brief Overview

9.2 One‐Shot Device Testing Data with Competing Risks

9.3 Likelihood Estimation for Exponential Distribution

9.3.1 Without Masked Failure Modes

9.3.2 With Masked Failure Modes

9.4 Likelihood Estimation for Weibull Distribution

9.5 Bayesian Estimation

9.5.1 Without Masked Failure Modes

9.5.2 Laplace Prior

9.5.3 Normal Prior

9.5.4 Dirichlet Prior

9.5.5 With Masked Failure Modes

9.6 Simulation Studies

9.7 Case Study with R Codes

10 One‐Shot Devices with Dependent Components. 10.1 Brief Overview

10.2 Test Data with Dependent Components

10.3 Copula Models

10.3.1 Family of Archimedean Copulas

10.3.2 Gumbel–Hougaard Copula

10.3.3 Frank Copula

10.4 Estimation of Dependence

10.5 Simulation Studies

10.6 Case Study with R Codes

11 Conclusions and Future Directions. 11.1 Brief Overview

11.2 Concluding Remarks. 11.2.1 Large Sample Sizes for Flexible Models

11.2.2 Accurate Estimation

11.2.3 Good Designs Before Data Analysis

11.3 Future Directions. 11.3.1 Weibull Lifetime Distribution with Threshold Parameter

11.3.2 Frailty Models

11.3.3 Optimal Design of SSALTs with Multiple Stress Levels

11.3.4 Comparison of CSALTs and SSALTs

Appendix A Derivation of

Appendix B Observed Information Matrix

Appendix C Non‐Identifiable Parameters for SSALTs Under Weibull Distribution

Appendix D Optimal Design Under Weibull Distributions with Fixed

Appendix E Conditional Expectations for Competing Risks Model Under Exponential Distribution

Appendix F Kendall's Tau for Frank Copula

Bibliography

Author Index

Index

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Data Collection And Analysis

Narayanaswamy Balakrishnan

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Table 1.3 Failure records on solder joints under CSALTs with temperature (K) and a dichotomous variable indicating if the PCB type is “copper‐nickel‐tin (CNT)” or not.

Source: Lau et al. (1988).

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