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An algorithm is developed for solving a broad class of performability models wherein system performance is identified with "reward." More precisely, for a system S and a utilization period T, the performance variable of the model is the reward derived from using S during T. The state behavior of S is represented by a finite-state stochastic process (the base model); reward is determined by reward rates associated with the states of the base model. Restrictions on the base model assume that the system in question is not repaired during utilization. It is also assumed that the corresponding reward model is a nonrecoverable process in the sense that a future state (reward rate) of the model cannot be greater than the present state. For this model class, we obtain a general method for determining the probability distribution function of the performance (reward) variable and, hence the performability of the corresponding system. Moreover, this is done for bounded utilization periods. The result is an integral expression which can be solved either analytically or numerically.