Stochastic Comparisons of Used Coherent System and New System of Used Components for Non-Identically Distributed and Dependent Components

Abstract

For components having dependent and possibly non-identically distributed lifetimes, we study the stochastic comparison between lifetimes of a used coherent system and a similar new system consisting of used components. Sufficient conditions for the usual stochastic order, the hazard rate order and the reversed hazard rate order under the situation when component lifetimes have general distribution are provided. As for proportional hazards component lifetimes, sufficient and necessary conditions guaranteeing several stochastic orders are derived, including the usual stochastic order, the hazard rate order, the reversed hazard rate order, the likelihood ratio order and the relative ageing orderings. Several numerical examples are provided for illustrations.