Heterogeneous standby systems with shocks-driven preventive replacements

The paper considers heterogeneous 1-out-of-N warm standby systems when all components can experience internal failures and operating components are exposed to external shocks. The components' resilience to shocks decreases with the number of experienced shocks. A preventive replacement policy when the operating component is replaced after it survives a certain number of shocks is considered. A numerical algorithm for evaluating the expected mission costs and the mission success probability is suggested. An optimization problem for a replacement policy that minimizes the expected mission cost providing a desired level of a mission success probability is formulated and solved. Illustrative examples are provided.