estimation of reliability in a random series system under exponentialdistribution

In this paper, the problem of estimating the reliability coefficient r =p(x > y ) in a series system with a random number of components is studied, whenthe life distribution of each component follows an exponential distribution and thenumber of components follows a geometric distribution. then, the point estimation ofr, based on maximum likelihood method is developed. the performance of the resultsis studied through a simulation study.