Mathematical Problems in Engineering
Volume 2005 (2005), Issue 2, Pages 151-163

Reliability for some bivariate gamma distributions

Saralees Nadarajah

Department of Statistics, University of Nebraska, Lincoln 68583, NE, USA

Received 23 July 2004; Revised 23 November 2004

Copyright © 2005 Saralees Nadarajah. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.