Optimal shock-driven switching strategies with elements reuse in heterogeneous warm-standby systems

Abstract

The paper considers heterogeneous 1-out-of-n warm-standby systems performing missions of a fixed duration when a failure of an operating element results in a mission failure. A system is operating in a random environment modeled by the Poisson process of shocks. Each shock can result in a failure of an operating element with probability that increases with the number of experienced shocks. Preventive replacement is used to reduce the probability of an operation failure. The standby elements experience the same shocks with a milder effect as they are partially shielded, which corresponds to a warm-standby mode. Elements after replacement can be reused again as standby elements. A new recursive algorithm for obtaining the mission success probability with reusable elements is suggested. This algorithm is used for determining the optimal sequence of replacements maximizing the mission success probability. A numerical example with detailed discussions is presented.