Conditional Inactivity Time of Components in a Coherent Operating System

The purpose of this paper is to study the conditional inactivity time of failed components of a coherent system consisting of n identical components with statistically independent lifetimes. Different aging and stochastic properties of this conditional random variable are obtained. Some mixture representations for the conditional inactivity time of the components are also derived. We give sufficient conditions based on the signature and the common distribution of component lifetimes to obtain stochastic ordering results for coherent systems. Some stochastic orders on the dynamic signature of coherent systems are also provided.