The art of progressive censoring. Applications to reliability and quality.

*(English)*Zbl 1365.62001
Statistics for Industry and Technology. New York, NY: Birkhäuser/Springer (ISBN 978-0-8176-4806-0/hbk; 978-0-8176-4807-7/ebook). xxi, 645 p. (2014).

This book offers a thorough and updated guide to the theory and methods of progressive censoring.

Progressive censoring can be described as a censoring method where units under test are removed from the life test at some prefixed or random inspection times. It allows for both failure and time censoring.

After introducing the basic notion and models of progressive censoring, the work presents a comprehensive treatment of distributional properties of progressively censored order statistics.

The material not only includes general results on joint, marginal, and conditional distributions and the dependence structure of the failure times, but also focuses on life distributions that are most important in applications (e.g., exponential and Weibull distributions). Further topics are moments, recurrence relations, characterizations, stochastic ordering, extreme value theory, simulation, and information measures like Fisher information and Shannon entropy.

The inferential topics cover linear, likelihood, and Bayesian inference in various models of progressive censoring. The authors discuss point and interval estimation for many life distributions as well as prediction problems. The discussion is completed by nonparametric inferential approaches and statistical tests including goodness-of-fit and precedence-type tests.

Finally, applications in survival analysis and reliability are provided. The presentation ranges from acceptance sampling, accelerated life testing including step-stress testing, stress-strength models, and competing risks to optimal experimental design.

The book has been written in a self-contained manner and, therefore, will be quite suitable either as a text for a graduate topic course, a text for a directed-reading course, or as a handbook on progressive censoring.

Progressive censoring can be described as a censoring method where units under test are removed from the life test at some prefixed or random inspection times. It allows for both failure and time censoring.

After introducing the basic notion and models of progressive censoring, the work presents a comprehensive treatment of distributional properties of progressively censored order statistics.

The material not only includes general results on joint, marginal, and conditional distributions and the dependence structure of the failure times, but also focuses on life distributions that are most important in applications (e.g., exponential and Weibull distributions). Further topics are moments, recurrence relations, characterizations, stochastic ordering, extreme value theory, simulation, and information measures like Fisher information and Shannon entropy.

The inferential topics cover linear, likelihood, and Bayesian inference in various models of progressive censoring. The authors discuss point and interval estimation for many life distributions as well as prediction problems. The discussion is completed by nonparametric inferential approaches and statistical tests including goodness-of-fit and precedence-type tests.

Finally, applications in survival analysis and reliability are provided. The presentation ranges from acceptance sampling, accelerated life testing including step-stress testing, stress-strength models, and competing risks to optimal experimental design.

The book has been written in a self-contained manner and, therefore, will be quite suitable either as a text for a graduate topic course, a text for a directed-reading course, or as a handbook on progressive censoring.

Reviewer: N. G. Gamkrelidze (Moskva)