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This paper presents a new algorithm for symbolic system reliability analysis. The method is applicable to system graphs with unreliable branches or nodes. Each branch is directed or undirected. Element probabilities need not be equal, but their failures are assumed to be s-independent. The new method makes no attempt to generate mutually exclusive events from the set of paths or cutsets but uses a technique to reduce greatly the number of terms in the reliability expression. Actual programming results show that the new method can efficiently handle systems having fewer than 20 paths or cutsets between the input-output node pair.