Reliability for discrete state systems with cyclic missions periods

Different regimes, for example, different seasons, bull market/bear market, multiple missions etc., affect the performance of systems or products greatly in the real world. Thus, a dynamic reliability model, with cyclic multiple mission periods, is developed for non-repairable discrete state systems in this paper. By taking Laplace transforms and aggregated stochastic theory for describing the conditional probabilities of transitions among different mission periods and system states, we obtain closed form solutions of some reliability indexes and distributions of sojourn times with perfect and imperfect function. Three models of valve systems are considered in details based on different reliability structures, and a numerical example of marine reactor safety water injection system is also presented by applying our proposed methods for two special cases: (i) when the mission durations are fixed and; (ii) when the mission durations have exponential distributions.