Reliability and Optimal Replacement Policy of a Multistate System Under Markov Renewal Shock Model

This article investigates the reliability and optimal replacement policy of a multistate system under the Markov renewal shock model, which has broad applications in engineering practice. The successive arrivals of shocks follow a continuous-time renewal process, and the system's state (damage) evolution is depicted as a homogeneous, irreducible Markov renewal process. In this context, the system incurs dual damages over time as follows: 1) one comes from the previous shocks' damage evolutions and 2) the other comes from the damage of successive arrivals of shocks. The reliability and optimal replacement time of the developed system are provided and the asymptotic evolution results for each shock, that is, the probabilities for each shock finally dissipating or causing the system's failure, are deduced. The optimal replacement policy for the developed shock model is discussed through minimizing the average cost rate function. Finally, numerical studies are given for the Markov renewal shock model, with interarrival times between adjacent shocks assumed to follow an exponential distribution.