Bounding network-reliability using consecutive minimal cutsets

A subset of consecutive minimal cutsets of the set of cutsets is used to develop an efficient algorithm to compute an upper bound for the reliability of a network. The reliability is the probability that a path consisting only of functioning arcs exists between the source and the sink of the network. The nodes of this network are perfect, but the arcs are independent and either function or fail with known probabilities. For the case of source-to-sink planar networks, an approach to obtain a lower bound for the reliability of the network is also presented. Examples illustrate the use of the algorithm and show that the upper bound is, is many cases, better than that obtained by A.W. Shogan (1976)