Reliability evaluation of Markov renewal shock models with multiple failure mechanisms

摘要

In this article, two Markov renewal shock models with multiple failure mechanisms are developed based on the extreme shock model and cumulative shock model respectively. The shock size and interarrival time dependency is studied by assuming the sizes and interarrival times of shocks are governed by an absorbing Markov chain with finite state space. Under the competing risk extreme shock model, the system fails when a single shock of a large size occurs or when it enters the absorbing state whichever occurs first. Under the competing risk cumulative shock model, the system fails when it transfers to the absorbing state, or when the accumulation of sizes of the previous shocks exceeds a prespecified critical level, whichever occurs first. The methods to calculate the reliability functions and other reliability indexes under the proposed two Markov renewal shock models are provided. A special case that the shock arrival process is independent of the current state of the system is considered. The limiting behavior of the mean time to failure of the system under two models is discussed. Finally, a study case of lithium-ion battery systems is conducted to illustrate the proposed models and obtained results.