Many real-world systems such as electric power transmission and distribution systems, transportation systems, and manufacturing systems can be regarded as flow networks whose arcs have independent, finite, and multivalued random capacities. Such a flow network is indeed a multistate system with multistate components and so its reliability for the system demand d , i.e., the probability that the maximal flow is no less than d , can be computed in terms of minimal path vectors to level d (named d-MPs here). The main objective of this paper was to present a simple algorithm to generate all d-MPs of such a system for each system capacity level d in terms of minimal pathsets. Analysis of our algorithm and comparison to Xue's algorithm shows that our method has the following advantages: (1 ) the family of d-MP candidates that it generates is smaller in size and so d-MPs can be generated more efficiently, (2) it is expressed more intuitively and so easier to understand, and (3) whenever applied in a seriesparallel case, both algorithms are essentially the same, but in a non series-parallel case, Xue's algorithm needs the extra work to transform the system into a series-parallel in advance. Two examples are illustrated to show how all d-MPs are generated by our algorithm and then the reliability of one example is computed. 0 7995 John Wiley & Sons, Inc.

& Conclusions-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 algosthm 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. 'Editors' note: To allow clear, easy reference, we have named the Xue algorithm [18] "XGMS" (Xue general multistate sytem), and the algorithm proposed "JLY" (Jane, Lin, Yuan).

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