Stochastic comparisons on conditional residual lifetime and inactivity time of coherent systems with exchangeable components

Abstract

The paper describes and develops two concepts of conditional residual lifetime of the system, given that at a fixed time a certain number of components have failed but still there are some functioning components, and conditional inactivity time of the failed components in the system, given that at that time a certain number of components have failed but the system is still alive. We consider the [Formula presented]-out-of-[Formula presented] and the coherent systems consisting of [Formula presented] components whose lifetimes are assumed to have an exchangeable joint distribution function. Some stochastic ordering results on the conditional residual lifetime and the conditional inactivity time are provided. Several illustrative examples are also given. © 2018 Elsevier B.V.