Mathematical Problems in Engineering
Volume 2005 (2005), Issue 1, Pages 101-111
doi:10.1155/MPE.2005.101
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) follows a bivariate distribution with dependence between
X and Y. In particular, we derive explicit expressions for R when the joint distribution is bivariate beta. The calculations
involve the use of special functions.