Reliability modeling and optimal maintenance strategies for stochastically deteriorating systems with random degradation latency

This paper mainly deals with the reliability modeling and optimal preventive replacement policies for a stochastically deteriorating system with random shocks. Specifically, the system is subject to stochastic performance deterioration, in which it is described with a Gamma process and degrades after a random degradation latency period. At the same time, a random shock process with a non-homogenous Poisson process is incorporated into system degradation modeling, where two kinds of shock effectiveness are formed upon arrival. The dependence between the degradation-induced failure and the shock-induced failure is bidirectional in this research. Based on system survival function, a periodic replacement policy and an inspection replacement policy are respectively investigated. The optimal solutions to the two preventive replacement policies are sought analytically and their resulting long-run average cost rates are compared to decide which one is more profitable. Finally, an illustrative example of the gas insulated transmission line is surveyed to validate the theoretical results, demonstrating that the random degradation onset time and two kinds of shocks are significant factors to system reliability evaluation and maintenance decisions.