Mean time to failure and availability of semi-Markov missions with maximal repair

We analyze mean time to failure and availability of semi-Markov missions that consist of phases with random sequence and durations. It is assumed that the system is a complex one with nonidentical components whose failure properties depend on the mission process. The stochastic structure of the mission is described by a Markov renewal process. We characterize mean time to failure and system availability under the maximal repair policy where the whole system is replaced by a brand new after successfully completing a phase before the next phase starts. Special cases involving Markovian missions are also considered to obtain explicit formulas.