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System reliability is the probability of the maximum flow in astochastic-flow network from the source node to the sink node being more than ademand level d. There are several approaches to compute system reliabilityusing upper boundary points, called d-MinCuts (d-MCs). Search for all the d-MCsin a stochastic-flow network is an NP-hard problem. Here, a work proposed byYeh [Yeh WC. A new approach to the d-MC problem. Reliab Eng and Syst Saf 2002;77(2): 201-206.] for determining all the d-MCs is investigated. Two results(Lemma 3 and Theorem 5) are shown to be incorrect and their correct versionsare established. Also, the complexity result (Theorem 6) is shown to beincorrect and the correct count is provided.

Technical Notes on "A new approach to the d-MC problem"