Reliability for some bivariate exponential distributions

Nadarajah, Saralees; Kotz, Samuel

doi:https://doi.org/10.1155/MPE/2006/41652

Mathematical Problems in Engineering

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Volume 2006 | Article ID 041652 | https://doi.org/10.1155/MPE/2006/41652

Reliability for some bivariate exponential distributions

Saralees Nadarajah¹and Samuel Kotz²

Received28 Jan 2005

Revised17 Mar 2005

Accepted20 Jun 2005

Published26 Feb 2006

Abstract

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

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Copyright

Copyright © 2006 Saralees Nadarajah and Samuel Kotz. 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.

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