Reliability for some bivariate exponential distributions

Abstract

In the area of stress-strength models, there has been a large amount of work as regards estimation of the reliabilityR=Pr⁡(X<Y). The algebraic form forR=Pr⁡(X<Y)has been worked out for the vast majority of the well-known distributions whenXandYare independent random variables belonging to the same univariate family. In this paper, forms ofRare considered when(X,Y)follow bivariate distributions with dependence betweenXandY. In particular, explicit expressions forRare derived when the joint distribution isbivariate exponential. The calculations involve the use of special functions. An application of the results is also provided.