Reliability For A Bivariate Gamma Distribution

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, we consider forms of R when ( X, Y ) follow a bivariate distribution with dependence between X and Y . In particular, we derive explicit expressions for R when the joint distribution is bivariate gamma. The calculations involve the use of special functions.