A new approach to the d-MC problem

Many real-world systems are multi-state systems composed of multi-state components in which the reliability can be computed in terms of the lower bound points of level d, called d-Mincuts (d-MCs). Such systems (electric power, transportation, etc.) may be regarded as flow networks whose arcs have independent, discrete, limited and multi-valued random capacities. In this paper, all MCs are assumed to be known in advance, and we focused on how to verify each d-MC candidate before using d-MCs to calculate the network reliability. The proposed algorithm is more efficient than existing algorithms. The algorithm runs in O(pσmn) time, a significant improvement over the previous O(pσm2) time bounds based on max-flow/min-cut, where p and σ are the number of MCs and d-MC candidates, respectively. It is simple, intuitive and uses no complex data structures. An example is given to show how all d-MC candidates are found and verified by the proposed algorithm. Then the reliability of this example is computed.