Sequential Bounding of the Reliability of a Stochastic Network

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Abstract
Given a directed source-sink network whose arcs either function or fail with known probabilities, we define the reliability of a node as the probability that there exists a path from the network's source to the node that consists only of functioning arcs. The concept of the strongly connected components of a network and the theory of associated random variables enable us to develop an algorithm that sequentially computes upper bounds on the reliabilities of nodes of the network until we finally obtain an upper bound on the reliability of the network's sink. The construction of a dual of the stochastic network permits the calculation of a lower bound on the reliability of the sink. These bounds are shown analytically to be tighter than the existing Esary-Proschan bounds.

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