Stochastic comparison on load‐sharing systems with one statistically dependent redundancy

Abstract

In this article, we study a load-sharing redundancy system in the presence of statistical dependence between base and redundancy component lifetimes when they are under partial workload. We derive the system reliability function in terms of reliability functions and the copula function of the base and redundancy component lifetimes. Further, in the setting of some aging properties, the base component and absolute continuous copula, we develop the hazard rate order, the reversed hazard rate order, and the likelihood ratio order between the system lifetime and the base component lifetimes. Two typical scenarios with independence between the base and redundancy component lifetimes are discussed in particular. Several numerical examples are presented to illustrate the theoretical findings as well.