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This paper presents an evaluation technique which is useful for studying both the performance and the reliability of a distributed computing system. The distributed system is evaluated the point of view of a user who submits a request for service. Our technique computes the average time to successful completion of this request, taking into account the system failures or repairs which may occur before the request is completed. Given a model of the system and its failures, the performance-reliability measures are computed in an automatic numerical fashion. The technique is computationally intensive, so it is limited to relatively small systems. However, it can produce results for many interesting cases without an inordinate amount of computation.