Computing Multi-State Two-Terminal Reliability Through Critical Arc States That Interrupt Demand

A variety of algorithms have been proposed to compute the NP-hard multi-state two-terminal reliability at demand level d (MS2TRd). Most of the methods solve the problem in terms of two to three NP-hard sub-problems. The only existing method that computes MS2TRd without requiring all multi-state minimal paths or cuts a priori, excluding the impractical complete enumeration method, and Doulliez & Jamoulle's popular but incorrect decomposition method, see P. Doulliez and E. Jamoulle, “Transportation networks with random arc capacities,” RAIRO, vol. 3, pp. 45-60, 1972, is the decomposition method proposed by Jane & Laih, see C.-C. Jane and Y.-W. Laith, “A practical algorithm for computing multi-state two-terminal reliability,” IEEE Trans. Reliability, vol. 57, pp. 295-302, 2008, recently. In contrast to Jane & Laih's method that computes MS2TRd in term of d-flows, this paper presents a novel decomposition method that computes 1-MS2TRd in terms of d-cuts. Contribution of the proposed method is that it is the first unique method that computes MS2TRd by way of cut sets without requiring all multi-state minimal paths or cuts a priori. An example illustrates the proposed algorithm. In addition, we make computational comparisons between the two algorithms in terms of d-flows, and d-cuts.