Reliability for some bivariate exponential distributions (Q610052)

Summary: In the area of stress-strength models, there has been a large amount of work as regards estimation of the reliability \(R=\text{Pr} (X <Y)\). The algebraic form for \(R = \text{PR} (X<Y)\) has been worked out for the vast majority of the well-known distributions when \(X\) and \(Y\) are independent random variables belonging to the same univariate family. In this paper, forms of \(R\) are considered when \((X, Y)\) follow bivariate distributions with dependence between \(X\) and \(Y\). In particular, explicit expressions for \(R\) are derived when the joint distribution isbivariate exponential. The calculations involve the use of special functions. An application of the results is also provided.