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) follows 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.