A Simple Method to Verify All d-Minimal Path Candidates of a Limited-Flow Network and its Reliability

Many real-world systems are multistate systems composed of multistate components in which the reliability can be computed in terms of minimal path (MP) vectors to level d (named d-MPs). Such systems (electric power, transportation, etc.) may be regarded as flow networks whose arcs have independent, discrete, limited, and multivalued random capacities. In this study, we focused on how to verify all the d-MP candidates before calculating the reliability value of a network. Based on the special property of d-MPs, we develop an intuitive algorithm which is better than the best-known existing method in verifying the d-MP candidates. Analysis of the proposed algorithm and comparison with existing algorithms shows that the proposed method is easier to understand and implement. Finally, an example is shown to illustrate how all d-MPs are generated and verified by the proposed algorithm. Then the reliability of this example is computed.