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Statistical Modeling and Robust Inference for One-shot Devices
- 1st Edition - April 1, 2025
- Authors: Narayanaswamy Balakrishnan, Elena Castilla
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 1 4 1 5 3 - 9
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 1 4 1 5 2 - 2
Statistical Modeling and Robust Interference for One-shot Devices offers a comprehensive investigation on robust techniques for one-shot devices under accelerated life tests. Wi… Read more
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Request a sales quoteStatistical Modeling and Robust Interference for One-shot Devices offers a comprehensive investigation on robust techniques for one-shot devices under accelerated life tests. With numerous examples, case studies, and included R codes in each chapter, this book helps readers implement their own codes, use them in proposed examples, and conduct their own research on one-shot device testing data. Researchers, mathematicians, engineers, and students working on accelerated life testing data analysis and robust methodologies will surely find this to be a welcomed resource.
The study of one-shot devices such as automobile airbags, fire extinguishers, and antigen tests is rapidly becoming an important problem in the area of reliability engineering. These devices, which get destroyed or must be rebuilt after use, are particular cases of extreme censoring, which makes the problem of estimating their reliability and lifetime challenging. As classical statistical and inferential methods do not consider the issue of robustness, this book is a welcomed addition to the conversation.
- Offers an in-depth review of statistical methods for the testing and analysis of one-shot devices
- Includes numerous examples and case studies in which the proposed methods are applied
- Introduces detailed R codes in each chapter to help readers implement their own codes, use them in proposed examples, and in their own research on one-shot device testing data
Graduate students, researchers, and professional mathematicians, statisticians, and engineers working on accelerated life testing data analysis and robust methodologies
1 Introduction
1.1 Brief Overview
1.2 Literature Survey on One-shot Devices
1.3 Some Examples
1.3.1 Electric Current
1.3.2 Solder Joints
1.3.3 Osteoporosis in Old People
1.3.4 Mice Tumors
1.3.5 Benzidine Dihydrochloride Experiment
1.3.6 Class-B Motor Insulation
2 Preliminaries
2.1 Brief Overview
2.2 Model Formulation and Likelihood Inference
2.2.1 ML Estimators
2.2.2 Confidence Intervals
2.2.3 Wald Tests
2.3 Bayesian Inference
2.4 Non-parametric Inference
2.5 One-shot device testing in R
3 Divergence Measures and their Application to One-shot Device Testing
3.1 Brief Overview
3.2 Motivation of Robust Inference for One-shot Devices
3.3 Weighted Minimum DPD Estimators
3.4 Divergence-based Confidence Intervals
3.5 Wald-type Tests
3.5.1 Power Function of the Wald-type Tests
3.6 Influence Functions
3.6.1 Influence Function of Weighted Minimum DPD Estmators
3.6.2 Influence Function of Wald-type Tests
3.7 On the Choice of the Optimal Tuning Parameter
4 Robust Inference under the Exponential Distribution
4.1 Brief Overview
4.2 Model Formulation
4.3 Weighted Minimum DPD Estimators
4.4 Wald-type Tests
4.5 Influence Function
4.6 Simulation Studies with R Codes
4.7 Case Studies with R Codes
5 Robust Inference under the Gamma Distribution
5.1 Brief Overview
5.2 Model Formulation
5.3 Weighted Minimum DPD Estimators
5.4 Wald-type Tests
5.5 Influence Function
5.6 Simulation Studies with R Codes
5.7 Case Studies with R Codes
6 Robust Inference under the Weibull Distribution
6.1 Brief Overview
6.2 Model Formulation
6.3 Weighted Minimum DPD Estimators
6.4 Wald-type Tests
6.5 Influence Function
6.6 Simulation Studies with R Codes
6.7 Case Studies with R Codes
7 Robust Inference under the Lognormal distribution
7.1 Brief Overview
7.2 Model Formulation
7.3 Weighted Minimum DPD Estimators
7.4 Wald-type Tests
7.5 Influence Function
7.6 Simulation Studies with R Codes
7.7 Case Studies with R Codes
8 Robust Inference under the Proportional Hazards Model
8.1 Brief Overview
8.2 Model Formulation
8.3 Weighted Minimum DPD Estimators
8.4 Wald-type Tests
8.5 Influence Function
8.6 Simulation Studies with R Codes
8.7 Case Studies with R Codes
9 Robust Inference under the Exponential Distribution and Competing Risks
9.1 Brief Overview
9.2 Model Formulation
9.3 Weighted Minimum DPD Estimators
9.4 Wald-Type Tests
9.5 Influence Function
9.6 Simulation Studies with R Codes
9.7 Case Studies with R Codes
10 Robust Inference under the Weibull Distribution and Competing Risks
10.1 Brief Overview
10.2 Model Formulation
10.3 Weighted Minimum DPD Estimators
10.4 Wald-type Tests
10.5 Simulation Studies with R Codes
10.6 Case Studies with R Codes
11 Robust Optimal Design of Accelerated Life Tests for One-Shot Device Testing
11.1 Brief Overview
11.2 Optimal Design of Experiment
11.3 Simulation Studies with R Codes
11.4 Case Studies with R Codes
12 Conclusions and Future Directions
12.1 Brief Overview
12.2 Concluding Remarks
12.3 Future Directions
12.3.1 Model validation
12.3.2 Non-destructive one-shot device testing
12.3.3 Rao-type Tests
1.1 Brief Overview
1.2 Literature Survey on One-shot Devices
1.3 Some Examples
1.3.1 Electric Current
1.3.2 Solder Joints
1.3.3 Osteoporosis in Old People
1.3.4 Mice Tumors
1.3.5 Benzidine Dihydrochloride Experiment
1.3.6 Class-B Motor Insulation
2 Preliminaries
2.1 Brief Overview
2.2 Model Formulation and Likelihood Inference
2.2.1 ML Estimators
2.2.2 Confidence Intervals
2.2.3 Wald Tests
2.3 Bayesian Inference
2.4 Non-parametric Inference
2.5 One-shot device testing in R
3 Divergence Measures and their Application to One-shot Device Testing
3.1 Brief Overview
3.2 Motivation of Robust Inference for One-shot Devices
3.3 Weighted Minimum DPD Estimators
3.4 Divergence-based Confidence Intervals
3.5 Wald-type Tests
3.5.1 Power Function of the Wald-type Tests
3.6 Influence Functions
3.6.1 Influence Function of Weighted Minimum DPD Estmators
3.6.2 Influence Function of Wald-type Tests
3.7 On the Choice of the Optimal Tuning Parameter
4 Robust Inference under the Exponential Distribution
4.1 Brief Overview
4.2 Model Formulation
4.3 Weighted Minimum DPD Estimators
4.4 Wald-type Tests
4.5 Influence Function
4.6 Simulation Studies with R Codes
4.7 Case Studies with R Codes
5 Robust Inference under the Gamma Distribution
5.1 Brief Overview
5.2 Model Formulation
5.3 Weighted Minimum DPD Estimators
5.4 Wald-type Tests
5.5 Influence Function
5.6 Simulation Studies with R Codes
5.7 Case Studies with R Codes
6 Robust Inference under the Weibull Distribution
6.1 Brief Overview
6.2 Model Formulation
6.3 Weighted Minimum DPD Estimators
6.4 Wald-type Tests
6.5 Influence Function
6.6 Simulation Studies with R Codes
6.7 Case Studies with R Codes
7 Robust Inference under the Lognormal distribution
7.1 Brief Overview
7.2 Model Formulation
7.3 Weighted Minimum DPD Estimators
7.4 Wald-type Tests
7.5 Influence Function
7.6 Simulation Studies with R Codes
7.7 Case Studies with R Codes
8 Robust Inference under the Proportional Hazards Model
8.1 Brief Overview
8.2 Model Formulation
8.3 Weighted Minimum DPD Estimators
8.4 Wald-type Tests
8.5 Influence Function
8.6 Simulation Studies with R Codes
8.7 Case Studies with R Codes
9 Robust Inference under the Exponential Distribution and Competing Risks
9.1 Brief Overview
9.2 Model Formulation
9.3 Weighted Minimum DPD Estimators
9.4 Wald-Type Tests
9.5 Influence Function
9.6 Simulation Studies with R Codes
9.7 Case Studies with R Codes
10 Robust Inference under the Weibull Distribution and Competing Risks
10.1 Brief Overview
10.2 Model Formulation
10.3 Weighted Minimum DPD Estimators
10.4 Wald-type Tests
10.5 Simulation Studies with R Codes
10.6 Case Studies with R Codes
11 Robust Optimal Design of Accelerated Life Tests for One-Shot Device Testing
11.1 Brief Overview
11.2 Optimal Design of Experiment
11.3 Simulation Studies with R Codes
11.4 Case Studies with R Codes
12 Conclusions and Future Directions
12.1 Brief Overview
12.2 Concluding Remarks
12.3 Future Directions
12.3.1 Model validation
12.3.2 Non-destructive one-shot device testing
12.3.3 Rao-type Tests
- No. of pages: 250
- Language: English
- Edition: 1
- Published: April 1, 2025
- Imprint: Academic Press
- Paperback ISBN: 9780443141539
- eBook ISBN: 9780443141522
NB
Narayanaswamy Balakrishnan
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.
Affiliations and expertise
Distinguished University Professor, Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, CanadaEC
Elena Castilla
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.
Affiliations and expertise
Assistant Professor, Rey Juan Carlos University, Madrid, Spain