The evaluation of network reliability and Fault Tree Analysis (FTA) is a NP-hard problem that is caused by sum-of-products. This paper presents a new algorithm for calculating system reliability by sum of disjoint products (SDP), based on Boolean algebra and generated from sum-of-products when minimal cut sets (MCS) are known. This algorithm could considerably reduce the number of disjoint (mutually exclusive) terms and save computation time with respect to top-event probability. Four major theorems of this algorithm are given, the use and correctness of which will be analyzed and proven. In addition, some examples for network reliability and FTA are illustrated to show the superiority and efficiency of the presented algorithm, which is not only easier to understand and implement but also better than the existing known SDP algorithm for large network and complex Fault Tree.
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