Unreliability evaluation for a limited-flow network with failed nodes subject to the budget constraint

This paper concentrates on a limited-flow network in which each node and branch has a designated capacity, which will have different lower levels due to various partial and complete failures. We try to evaluate the system unreliability that the maximum flow of the network is less than or equal to the demand d without exceeding the budget B. First, a simple algorithm in terms of minimal cuts is proposed to generate all (d, B)-MCs in order to evaluate the system unreliability. A computer example is shown to illustrate the solution procedure.