On the Mean and Variance Residual Life Comparisons of Coherent Systems with Identically Distributed Components

Abstract

The problem of stochastic comparison of two coherent systems has received a great attention in recent years. In the present work, we study the stochastic comparison of coherent systems with identically distributed (ID) components. We use the copula function to explore the structural dependency of the components. The comparison results are obtained based on the notion of distorted distributions. We focus on the residual lifetime orders and obtain comparison results for the mean and variance residual life orders of coherent systems with ID component lifetimes. In the sequel, we study ageing faster orders in the mean and variance residual lifetime and provide some sufficient conditions such that one coherent system dominates another system with respect to the proposed orders. Some illustrative examples are also given to demonstrate the theoretical results.