Estimation of system reliability from stress-strength relationship

In this paper, we estimate the reliability of parallel system with two components. We assume that strengths of these components follow a bi-variate exponential(BVE) distribution. These two components are subjected to a common stress which is independent of the strength of the components. If the strengths (X1,X2) are subjected to a common random stress(Y), then the reliability of a system or system reliability (R) is given by R = P[Y < Max(X1,X2)]- We estimate R when (X1,X2) have different BVE models proposed by Marshall-01kin(1967), Block-Basu(1974), Freund(1961) and Proschan-Sullo(1974). The distribution of Y is assumed to be either exponential or gamma. The asymptotic normal(AN) distributions of these estimates are obtained. We present a numerical study for obtaining MLE of R in all four BVE models when the common stress (Y) is exponentially distributed.