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

AbstractIn 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.Keywords: Bayes estimateHPD credible intervalLehmann family of distributionsmaximum likelihood estimateMCMC methodsimple step-stress life testTRV model2010 MATHEMATICS SUBJECT CLASSIFICATION: 62N0262F1062F15 ACKNOWLEDGMENTSThe authors thank the Associate Editor and an anonymous reviewer for their positive remarks and useful comments. The first and third authors thank the Department of Mathematics, National Institute of Technology Rourkela, India, for the available research facilities.DISCLOSUREThe authors have no conflicts of interest to report.Additional informationFundingS. Dutta thanks the Council of Scientific and Industrial Research (C.S.I.R., Grant No. 09/983(0038)/2019-EMR-I), India, for the financial assistance received to carry out this research work.