Estimation of reliability in a series system with random sample size

In this paper, we are interested in the estimation of the reliability coefficient R=P(X>Y)R=P(X>Y), when the data on the minimum of two exponential samples, with random sample size, are available. The confidence intervals of RR, based on maximum likelihood and bootstrap methods, are developed. The performance of these confidence intervals is studied through extensive simulation. A numerical example, based on a real data, is presented to illustrate the implementation of the proposed procedure.