On the residual lifetimes of coherent systems with exchangeable components

Abstract

For practical applications in reliability analysis, the assumption of dependence among lifetimes of components of the system is more realistic than the assumption of independence. This paper investigates the residual lifetimes of coherent systems in situation where there exists a stochastic dependence among the components of the system. A stochastic comparison among residual lives of k-out-of-n systems with exchangeable components is conducted. The mean residual life function of a k-out-of-n system with exchangeable components is investigated. Special examples in the case of a system consisting of two dependent components with a joint Gumbel's bivariate exponential distribution and for a system having n components with Marshall and Olkin's multivariate exponential distribution, illustrating the behavior of the mean residual life function are provided. The extension to general coherent systems with exchangeable components using properties of Samaniego's signature are given. © 2012 Pakistan Journal of Statistics.