Statistics, Department of


Date of this Version



Mathematical Problems in Engineering Volume 2006, Article ID 41652, Pages 1–14


Copyright © 2006 S. Nadarajah and S. Kotz.

Open access

DOI 10.1155/MPE/2006/41652


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 is bivariate exponential. The calculations involve the use of special functions. An application of the results is also provided.