Estimation of reliability for multi-component stress–strength model based on modified Weibull distribution

This paper is devoted to estimating the reliability of a multi-component stress–strength model in an s-out-m (s≤m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s \le m$$\end{document}) system under progressively type-II censored modified Weibull data. This type of systems functions only if at least s out of m strengths exceed the stress. Maximum likelihood and Bayes estimators of the stress–strength reliability based on conjugate prior are obtained. The associated confidence and credible intervals are also developed. The Lindley’s approximation and Markov chain Monte Carlo methods are used to compute approximate Bayes estimates. Two real data sets representing the excessive drought of Shasta Reservoir in California, USA and failure times of software model are analyzed for illustrative purposes. Further, Monte Carlo simulations are performed to compare the so developed estimates.