Mean time to finish a randomly disturbed 2-phase mission

This paper shows the average time to finish a mission consisting of a sequence of two noninterruptible phases of deterministic, given lengths, when after a short disturbance the interrupted phase has to be restarted. Disturbances, e.g., intermittent faults, are modeled according to a renewal point-process. In order to overcome limitations of Markov modeling, this point process need not be Poisson. Fairly simple closed-form solutions are derived. The Poisson case treated, is a practical example. Upper bounds are derived for easy conservative approximations. The approach can be easily extended to cover the determination of probability distributions instead of only mean values