Reliability for some bivariate exponential distributions

Abstract

In the area of stress‐strength models, there has been a large amount of work as regards estimation of the reliability R = Pr ⁡( X < Y ). The algebraic form for R = 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.