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A reliability analysis method for computing systems is considered in which the underlying criteria for "success" are based on the computations the system must perform in the use environment. Beginning with a general model of a "computer with faults," intermediate concepts of a "tolerance relation" and an "environment space" are introduced which account for the computational needs of the user and the probabilistic nature of the use environment. These concepts are then incorporated to obtain a precisely defined class of computation-based reliability measures. Formulation of a particular measure is illustrated and results, applying this measure, are compared with those of a typical structure-based analysis.