Multistate network reliability evaluation under the maintenance cost constraint

Many real-world systems (such as electric power, transportation, etc.) are multistate systems composed of multistate components. Such systems may be regarded as flow networks whose arcs have independent, discrete, limited and multivalued random capacities. Their reliability can be computed in terms of minimal cut (MC) vectors to level (d,c) (named (d,c)-MCs here), using the probability that d units of flow can be transmitted from the source node to the sink node such that the total maintenance cost of each d-MCs is less than or equal to c. In this study, all MCs are assumed to be known in advance and we developed an intuitive algorithm based on some simple concepts that were found in this study to find the entire (d,c)-MCs before calculating the reliability value of a network. One example is illustrated to show how all (d,c)-MCs are generated by the proposed algorithm. Then the reliability of this example is computed. The computational complexity of the proposed algorithm is also analyzed.