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The study of one-shot devices such as automobile airbags, fire extinguishers, or antigen tests, is rapidly becoming an important problem in the area of reliability engineering. These devices, which are destroyed or must be rebuilt after use, are a particular case of extreme censoring, which makes the problem of estimating their reliability and lifetime challenging. However, classical statistical and inferential methods do not consider the issue of robustness.
Statistical Modeling and Robust Interference for One-shot Devices offers a comprehensive investigation of robust techniques of one-shot devices under accelerated-life tests. With numerous examples and case studies in which the proposed methods are applied, this book includes detailed R codes in selected chapters to help readers implement their own codes and use them in the proposed examples and in their own research on one-shot devicetesting data. Researchers, mathematicians, engineers, and students working on acceleratedlife testing data analysis and robust methodologies will find this to be a welcome resource.
List of contents
1. Introduction
2. Inference for One-Shot Devices with a Single Failure mode
3. Divergence Measures and their Application to One-Shot Devices with a Single Failure mode
4. Robust Inference under the Exponential Distribution
5. Robust Inference under the Gamma Distribution
6. Robust Inference under the Weibull Distribution
7. Robust Inference under the Lognormal distribution
8. Robust Inference under the Proportional Hazards Model
9. Inference for One-Shot Devices with Multiple Failure Modes
10. Robust Inference under the Exponential Distribution and Competing Risks
11. Robust Inference under the Weibull Distribution and Competing Risks
12. Robust Inference under Cyclic Accelerated Life Tests
13. Summary and Future Directions
Appendix A Derivation of the Influence Function of the Weighted Minimum DPD Estimators
About the author
Narayanaswamy Balakrishnan is a distinguished university professor in the Department of Mathematics and Statistics at McMaster University Hamilton, Ontario, Canada. He is an internationally recognized expert on statistical distribution theory, and a book-powerhouse with over 24 authored books, four authored handbooks, and 30 edited books under his name. He is currently the Editor-in-Chief of Communications in Statistics published by Taylor & Francis. He was also the Editor-in-Chief for the revised version of Encyclopedia of Statistical Sciences published by John Wiley & Sons. He is a Fellow of the American Statistical Association and a Fellow of the Institute of Mathematical Statistics. In 2016, he was awarded an Honorary Doctorate from The National and Kapodistrian University of Athens, Athens, Greece. In 2021, he was elected as a Fellow of the Royal Society of Canada.Elena Castilla is an assistant professor at the Department of Applied Mathematics at Rey Juan Carlos University, in Spain. She obtained her Ph.D, M.Sc. and Bachelor Degrees in Mathematics and Statistics at Universidad Complutense de Madrid, and is an awardee of the Ramiro Melendreras Award (SEIO, 2021) and Vicent Caselles Award (RSME & Fundación BBVA 2022). Dr. Castilla’s research interests include information theory, categorical data analysis, composite likelihood, logistic regression models, reliability analysis and robust statistics.
