Reliability for extreme value distributions

In the area of stress-strength models there has been-a large amount of work as regards estimation of the reliability R = Pr(X-2 < X-1) when X-1 and X-2 are independent random variables belonging to the same univariate family of distributions. The algebraic form for R = Pr(X-2 < X-1) has been worked out for the majority of the well-known distributions in the standard forms. However, there are still many other distributions (including generalizations of the well-known distributions) for which the form of R is not known. We have identified at least some 30 distributions with no known form for R. In this paper, we consider-the class of extreme value distributions (including the Pareto distributions) and derive the corresponding forms for the reliability R. The calculations involve the use of special functions. (C) 2003 Elsevier Science Ltd. All rights reserved.