Estimation of Stress-Strength Reliability for Quasi Lindley Distribution

Abstract

This paper discussed the problem of stress-strength reliability model R=Pr(Y< X). It is assumed that the strength of a system X, and the environmental stress applied on it Y, follow the Quasi Lindley Distribution(QLD). Stress-strength reliability is studied using the maximum likelihood, and Bayes estimations. Asymptotic confidence interval for reliability is obtained. Bayesian estimations were proposed using two different methods: Importance Sampling technique, and MCMC technique via Metropolis-Hastings algorithm, under symmetric loss function (squared error) and  asymmetric loss functions (linex, general entropy). The behaviors of the maximum likelihood and Bayes estimators of stress-strength reliability have been studied through the Monte Carlo simulation study.