Bayesian Inference for Weibull Distribution under the Balanced Joint Type-II Progressive Censoring Scheme

Abstract

SYNOPTIC ABSTRACT Progressive censoring schemes have received considerable attention recently. All of these developments are mainly based on a single population. Recently, Mondal and Kundu (2016) introduced the balanced joint progressive censoring scheme (BJPC), and studied the exact inference for two exponential populations. It is well known that the exponential distribution has some limitations. In this article, we implement the BJPC scheme on two Weibull populations with the common shape parameter. The treatment here is purely Bayesian in nature. Under the Bayesian set up we assume a Beta Gamma prior of the scale parameters, and an independent Gamma prior for the common shape parameter. Under these prior assumptions, the Bayes estimators cannot be obtained in closed forms, and we use the importance sampling technique to compute the Bayes estimators and the associated credible intervals. We further consider the order restricted Bayesian inference of the parameters based on the ordered Beta Gamma priors of the scale parameters. We propose one precision criteria based on expected volume of the joint credible set of model parameters to find out the optimum censoring scheme. We perform extensive simulation experiments to study the performance of the estimators, and finally analyze one real data set for illustrative purposes.