Performance measures for systems with Markovian missions and aging

We consider a mission-based reliability system that is designed to perform missions consisting of a random sequence of phases or stages with random durations. The mission process is described by a Markov process, and the deterioration of the system is described by a finite state Markov process whose parameters depend on the mission process. We discuss several performance measures, including mission reliability, phase reliability, as well as mean residual life and availability. We derive explicit computational formulas, and provide an illustration. We also show how our model can be applied to any coherent system with s-independent and exponentially distributed component lifetimes