Phase-type stress-strength reliability models under progressive type-II right censoring

Abstract

. The study of stress-strength reliability estimation based on phase-type distribution helps to gather results on estimation of stress-strength reliability with any probability distribution that is defined on the non negative real numbers as any discrete or continuous probability distributions on the positive real line can be represented as phase-type. The matrix representation of the parameters of phase-type distributions helps in their flexible evaluation and easy manipulation. Also in many of the experimental studies, it is very convenient and useful to apply progressive type-II right censoring mechanism in the process of data collection. In this article, we consider the estimation of stress-strength reliability (R) based on phase-type distribution under progressive type-II right censoring mechanism. Both stress and strength random variables are assumed to follow either continuous phase-type or discrete phase-type distribution. We have developed the algorithm for computing Maximum likelihood estimate (MLE) of R based on the expectation maximization (EM) method and the Bayes estimate of R using Markov Chain Monte Carlo technique. A detailed numerical illustration using simulated data/ real data sets are carried out.