On the copula-based reliability of stress-strength model under bivariate stress

Abstract

In this paper, we consider the stress-strength reliability R = P ( X 1 < Y < X 2 ) where the strength Y of a component lies between the dependent stress variables X 1 and X 2 . We propose a copula-based approach for stress-strength reliability having bivariate stress. We obtain R for Farlie-Gumbel-Morgenstern copula with Burr III marginals. Also, we propose a Bernstein copula approximation for evaluating R under the stress-strength setup. We present empirical and maximum likelihood-based estimation procedures and compare their performances by Monte Carlo simulation. We apply the proposed approach to chemical and overt diabetes data for illustration purpose.