Reliability evaluation of multistate networks: An improved algorithm using state-space decomposition and experimental comparison

This article introduces an improved algorithm using State-Space Decomposition for exact reliability evaluation of multistate networks given all minimal path vectors (d-MPs for short). We make two main contributions to the area. First, during each recursive call for the decomposition process, we find that the set of d-MPs can be decomposed recursively, and only those qualified d-MPs from a previous set of unspecified states are needed. Second, an improved heuristic rule is proposed choose an appropriate d-MP to decompose each set of unspecified states. Then, efficiency investigations of the proposed algorithm are conducted using hypothetical networks by changing one of the following network parameters while fixing the others, namely, the number of components, the number of d-MPs, and the number of states for each component. Efficiency investigations on networks with known structures are also conducted. Based on the computational experiments, it is found that (i) the proposed algorithm is more efficient than existing algorithms using the state-space decomposition method; (ii) the proposed algorithm is more efficient than existing algorithms using the Recursive Sum of Disjoint Products method when the number of d-MPs is not too small; and (iii) the indirect approach incorporating the proposed algorithm is more efficient than existing direct approaches. Guidelines for choosing the appropriate algorithm are provided. In addition, an algorithm is developed for network reliability evaluation given all minimal cut vectors (d-MCs for short).