Using minimal cuts to evaluate the system reliability of a stochastic-flow network with failures at nodes and arcs

Yi-Kuei Lin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

128 Scopus citations


This paper deals with a stochastic-flow network in which each node and arc has a designated capacity, which will have different lower levels due to various partial and complete failures. We try to evaluate the system reliability that the maximum flow of the network is not less than a demand (d+1). A simple algorithm in terms of minimal cuts is first proposed to generate all upper boundary points for d, and then the system reliability can be calculated in terms of such points. The upper boundary point for d is a maximal vector, which represents the capacity of each component (arc or node), such that the maximum flow of the network is d. A computer example is shown to illustrate the solution procedure.

Original languageEnglish
Pages (from-to)41-46
Number of pages6
JournalReliability Engineering and System Safety
Issue number1
StatePublished - 1 Jan 2002


  • Minimal cut
  • Node failure
  • Stochastic-flow network
  • System reliability
  • Upper boundary point for d

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