RELIABILITY EVALUATION OF A LIMITED-FLOW NETWORK IN TERMS OF MINIMAL CUTSETS

Many systems can be regarded as flow networks whose arcs have discrete and multi-valued random capacities. The probability of the maximum flow at each various level and the reliability of such a flow network can be calculated in terms of K-lattices which are generated from each subset of the family of all MCs (minimal cutsets). However the size of such a family 2m - 1 (m = number of MCs) grows exponentially with m. Such a flow network can be considered as a multistate system with multistate components so that its reliability can be evaluated in terms of upper boundary points of each level d (named d-MCs here). This article presents an algorithm to generate all d-MCs from each MC for each system capacity level d. After analyzing and comparing it with the algorithm by Xue, it ensures that our method generates a family of d-MC candidates which contains all d-MCs more efficiently if both start from MCs. Examples show how all d-MCs are generated; the reliability of one example is computed.