An efficient method for reliability evaluation of multi-state networks given all minimal path vectors

The multi-state networks under consideration consist of a source node, a sink node, and some independent failure prone components in between. The components can work at different levels of capacity. For such a network, we are interested in evaluating the probability that the flow from the source node to the sink node is equal to or greater than a demanded flow of d units. A general method for reliability evaluation of such multi-state networks is using minimal path (cut) vectors. A minimal path vector to system state d is called a dMPs. Given that all d-MPs have been found, the issue becomes how to evaluate the probability of the union of the events that the component state vector is greater than or equal to at least one of the d-MPs. In this paper, we report an efficient recursive algorithm for this union probability evaluation based on the sum of disjoint products (SDP) principle, and name it the Recursive Sum of Disjoint Products (RSDP) algorithm. RSDP provides us with an efficient, systematic and simple approach for evaluating multi-state two-terminal network reliability given all d-MPs.