Adaptive Progressive Censoring in Reliability and Survival Analysis: Methods, Design, and Practice

Abstract

Incomplete lifetime data frequently arise in reliability and survival experiments due to constraints in cost, time, and operational conditions. To address these challenges, several advanced censoring schemes have been developed to enhance testing efficiency and improve the accuracy of statistical inference. This review provides a unified framework for adaptive progressive censoring and its extensions, including adaptive progressive Type-II hybrid censoring, adaptive progressive Type-I hybrid censoring, adaptive general progressive Type-II hybrid censoring, improved adaptive progressive Type-II hybrid censoring, and adaptive progressive first-failure censoring schemes. The paper summarizes their design methodologies, likelihood and spacings-based formulations, and the main inferential approaches under classical, Bayesian, and expected Bayesian paradigms. Applications involving multiple causes of failure, accelerated life testing experiments, block and joint censoring structures, and random removals are also discussed. The review further highlights the practical balance among experimental duration, cost, and estimation precision, and identifies several promising directions for future research, such as dependent competing risks, optimal censoring design, and computational developments for modern reliability and survival analysis, that may be of interest to investigators seeking further advancements in this area.