Statistics, Department of


Date of this Version



Mathematical Problems in Engineering 2005:2 (2005) 151–163


Copyright © 2005 Hindawi Publishing Corporation

DOI: 10.1155/MPE.2005.151


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.