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This paper developes two algorithms for finding the time-dependent reliability of any active-redundant system in terms of component failure probabilities. These algorithms apply to non-loaded, continuously-operating systems in which drift-type failures are neglected. The first algorithm is used when each component can fail in only one mode. A procedure, based on the Quine-McCluskey technique from switching circuit theory, is stated in conjunction with this algorithm which permits rapid simplification of the reliability expression. Two failure modes are permitted in the second algorithm. The relation between the expressions resulting from the algorithms and lifetime random variables is given so that the algorithms do not depend on specific component failure distributions.