Institute of Mathematics and Informatics Bulgarian Academy of Sciences
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 including
Normal, uniform, exponential, gamma, weibull and pareto. However,
there are still many other 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 some of these distributions and derive
the corresponding forms for the reliability R. The calculations involve the
use of various special functions
