Stochastic Comparisons of Lifetimes of Two Series and Parallel Systems with Location-Scale Family Distributed Components having Archimedean Copulas

Abstract: In this paper, we compare the lifetimes of two series and two parallel systems stochastically where the lifetime of each component follows location-scale (LS) family of distributions. The comparison is carried out under two scenarios: one, that the components of the systems have a dependent structure sharing Archimedean copula and two, that the components are independently distributed. It is shown that the systems with components in series or parallel sharing Archimedean copula with more dispersion in the location or scale parameters results in better performance in the sense of the usual stochastic order. It is also shown that if the components are independently distributed, it is possible to obtain more generalized results as compared to the dependent set-up. The results in this paper generalizes similar results in both independent and dependent set up for exponential and Weibull distributed components.