Estimation of reliability in a parallel system with random sample size

In this paper, we derive the distribution of life length of a parallel system with random number of components when the life distribution of each component follows a Weibull distribution and the number of components follows a Poisson distribution truncated at zero. For two independent such parallel systems, we are interested in the estimation of the reliability parameter R=P(X>Y), where X and Y are the life lengths of the two parallel systems. The point estimate and confidence interval of R, based on maximum likelihood method, are developed. The performance of each of the point estimate and confidence interval of R is studied through extensive simulation study. A numerical example, based on a real data, is presented to illustrate the implementation of the proposed procedure.