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This paper addresses a stochastic-#ow network in which each arc or node has several capacities and may fail. Given the demand d, we try to evaluate the system reliability that the maximum #ow of the network is not less than d. A simple algorithm is proposed "rstly to generate all lower boundary points for d, and then the system reliability can be calculated in terms of such points. One computer example is shown to illustrate the solution procedure.-This paper addresses a stochastic-#ow network in which each arc or node has several capacities and may fail. Given the demand d, we try to evaluate the system reliability that the maximum#ow of the network is not less than d. A simple algorithm is proposed "rstly to generate all lower boundary points for d, and then the system reliability can be calculated in terms of such points. One computer example is shown to illustrate the solution procedure.