Bayesian and non-Bayesian inference for a general family of distributions based on simple step-stress life test using TRV model under type II censoring

• Published in: Sequential analysis Vol. 42; no. 4; pp. 349 - 370
• Main Authors: Dutta, Subhankar, Sultana, Farha, Kayal, Suchandan
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02.10.2023; Taylor & Francis Ltd
• Subjects: Bayes estimate; Bayesian analysis; Confidence intervals; Fisher information; HPD credible interval; Lehmann family of distributions; Markov chains; Mathematical models; maximum likelihood estimate; Maximum likelihood estimators; MCMC method; Model testing; Normal stress; Parameters; Parametric statistics; Random variables; simple step-stress life test; Statistical inference; TRV model
• ISSN: 0747-4946; 1532-4176
• DOI: 10.1080/07474946.2023.2224401

In this article, we consider the parametric inference, using Type II censored data, based on the tampered random variable (TRV) model for simple step-stress life testing (SSLT). We have taken the members of the Lehmann family of distributions as the baseline lifetimes of the experimental units under normal stress conditions. Based on Type II censored data and a simple SSLT framework, we obtain the maximum likelihood estimator (MLE) and the Bayes estimators of the model parameters. Further, we obtain asymptotic confidence intervals of the unknown model parameters using the observed Fisher information matrix. Moreover, bootstrap confidence intervals were constructed. The Bayes estimators are computed using the Markov chain Monte Carlo (MCMC) method under the squared error loss function and the LINEX loss function. We also construct the highest posterior density (HPD) credible intervals of the unknown model parameters. Extensive simulation studies are performed to investigate the finite sample properties of the proposed estimators. Finally, the proposed methods are illustrated with the analysis of a real data set.