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In this paper, we present an algebraic technique for computing the system reliability of a complex system. And we also studied the problem of inverting minimal path sets to obtain minimal cut sets of the complex system. We described efficiency of inversion algorithm by the use of Boolean algebra and we developed an inclusion-exclusion algorithm and a pivotal decomposition algorithm for the reliability calculation of the complex system. We verified that inclusion-exclusion algorithm is more useful than pivotal decomposition algorithm in series structure. Otherwise, pivotal decomposition algorithm is more useful than inclusion-exclusion algorithm in parallel structure. Several examples are illustrated and the computation speeds between the two algorithms are undertaken. Keywords-system reliability; boolean algebra; inversion algorithm; inclusion-exclusion algorithm; pivotal decomposition algorithm

Algorithms for Reliability Calculation of Complex Bridge System