Abstract
A combinatorial approach to reliability preserving transformation of stochastic networks is presented. It involves splitting the underlying graph G into two edge-disjoint subgraphs, carrying out separate reliability analyses for the arising two stochastic subnetworks, and combining the results to obtain a formula for the reliability of the original stochastic network. Based on this decomposition formula, a general approach to reliability preserving network transformation is proposed. Its principle idea consists in simplifying the topological structure of G by substituting one of the subgraphs specified by the decomposition process with one or more partial replacement graphs. The corresponding stochastic replacement networks are determined in such a way that the reliability of the original stochastic network is retained. Special attention is given to the construction of suitable replacement graphs. The case of a 3-point separating node set is considered in more detail.
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