RELIABILITY FOR SOME BIVARIATE EXPONENTIAL 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 < 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 var...

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Bibliographic Details
Published in:Mathematical Problems in Engineering 2006-01, Vol.2006, p.420-433
Main Authors: Nadarajah, Saralees, Kotz, Samuel
Format: Article
Language:English
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Summary: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.
ISSN:1024-123X
1563-5147
DOI:10.1155/MPE/2006/41652