Bayesian Analysis Using Joint Progressive Type-II Censoring Scheme

The joint censoring technique becomes crucial when the study's aim is to assess the comparative advantages of products concerning their service times. In recent years, there has been a growing interest in progressive censoring as a means to reduce both cost and experiment duration. This article delves into the realm of statistical inference for the three-parameter Burr-XII distribution using a joint progressive Type II censoring approach applied to two separate samples. We explore both maximum likelihood and Bayesian methods for estimating model parameters. Furthermore, we derive approximate confidence intervals based on the observed information matrix and employ four bootstrap methods to obtain confidence intervals. Bayesian estimators are presented for both symmetric and asymmetric loss functions. Since closed-form solutions for Bayesian estimators are unattainable, we resort to the Markov chain Monte Carlo method to compute these estimators and the corresponding credible intervals. To assess the performance of our estimators, we conduct extensive simulation experiments. Finally, to provide a practical illustration, we analyze a real dataset.