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An algorithm is described for solving the reliability model of a repairable system of n identical components placed in a fluctuating 2-state environment. An important application is where the effects of alternating normal and severe weather conditions are to be evaluated. A modified version of the algorithm can accommodate the case where faults are followed by switching operations, as in power transmission networks. Whereas the standard Markov method to solve such models is cumbersome and other available methods are often limited in scope, the proposed algorithm is fast, reasonably accurate, and does not require a computer.