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 R R , 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.
series system random sample size truncated poisson distribution asymptotic and bootstrap confidence intervals simulation study