Resilience analysis of four-state engineering systems under the framework of continuous-time Markov chain model

For engineering systems, resilience measures the ability of the system to resist and recover from disruptive events. In the recent literature, the vast majority of studies devoted to resilience measures taking the form of probability and can only be computed by simulation. This study deals with resilience of four-state engineering systems under the framework of continuous-time Markov chain model. We derive closed-form expressions of three resilience metrics: the survival function of the resistance time to system failure before recovery, the probability of recovery to the perfect state before system breakdown, and the survival function of the recovery time before system breakdown. In addition, we present some analytical results on these resilience metrics, which shed a light on improving system resilience. Also, we illustrate this approach based on simulation and a real application.