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Mathematical Problems in Engineering
Volume 2004, Issue 2, Pages 169-183
http://dx.doi.org/10.1155/S1024123X0431104X

Reliability for Laplace distributions

Department of Mathematics, University of South Florida, Tampa 33620-5700, FL, USA

Received 30 October 2003

Copyright © 2004 Hindawi Publishing Corporation. 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.

Abstract

In the area of stress-strength models there has been a large amount of work as regards estimation of the reliability R=Pr(X2<X1) when X1 and X2 are independent random variables belonging to the same univariate family of distributions. The algebraic form for R=Pr(X2<X1) 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 has not been derived. In this paper, we consider several Laplace distributions and derive the corresponding forms for the reliability R. The calculations involve the use of special functions.