Bayesian reliability analysis of Weibull data from multiple facilities under a new block unified hybrid censoring scheme

Abstract

Abstract In terms of block sample methodology, this paper introduces a new block censoring scheme called block unified hybrid censoring. This block plan can be considered as a generalized censoring scheme for some existing block censoring schemes, such as block Type-II censoring and block hybrid censoring. The proposed block plan ensures that the experiment ends with at least a prefixed number of failures, which increases the statistical efficiency compared to other block censoring schemes like block hybrid censoring, where the test may be terminated with few failures or even no failures at all. We investigate the maximum likelihood and Bayesian estimation of the Weibull distribution and three of its reliability metrics. The classical point and approximate confidence intervals are considered, while the Bayes estimators using the squared error loss function and highest posterior density credible intervals are also examined. Another important issue in block samples is the evaluation of differences among various test facilities. In addition, a coverage similarity index is introduced to quantify facility similarity through the degree of overlap among the interval estimates of the facility-specific scale parameters, with larger values indicating greater similarity. A simulation study with various sampling designs is implemented to compare the different estimation methods. Finally, we consider two applications to cancer datasets to demonstrate the importance of the proposed scheme as well as the proposed methods.