Stress-strength model of m-components system in censored data

Abstract

In this paper, we consider the statistical estimation using Bayesian inference for a multi-component stress-strength parameter. This involves non-identical component strengths under a progressive censoring scheme, within the context of the exponentiated Weibull distribution. The paper addresses the problem in three scenarios. Firstly, it assumes that stress and strength share two common and unknown parameters, along with one unknown different parameter. To obtain the Bayes estimate, the paper utilizes the Markov Chain Monte Carlo (MCMC) method. Secondly, in the scenario where stress and strength share two common and known parameters, along with one unknown different parameter, the paper employs the MCMC method and Lindley’s approximation. Thirdly, in the general case, the paper utilizes the MCMC method to obtain the Bayes estimate. A Monte Carlo simulation study is used to compare various estimates. An application concerning monthly water capacities of the Shasta reservoir in California is finally provided.