The Creation Process is an algorithm that transforms a static network model into a dynamic one. It is the basis of different variance reduction methods designed to make efficient reliability estimations on highly reliable networks in which links can only assume two possible values, operational or failed. In this article the Creation Process is extended to let it operate on network models in which links can assume more than two values. The proposed algorithm, called here Multi-Level Creation Process, is the basis of a method, also introduced here, to make efficient reliability estimations of highly reliable stochastic flow networks. The method proposed, which consists in an application of Splitting over the Multi-Level Creation Process, is empirically shown to be accurate, efficient, and robust.

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A stochastic binary system (SBS) is a multicomponent on‐off system subject to random independent failures on its components. After potential failures, the state of the subsystem is ruled by a logical function (called structure function) that determines whether the system is operational or not. A SBS serves as a natural generalization of network reliability analysis, where the goal is to find the probability of correct operation of the system (in terms of connectivity, network diameter, or different measures of success). A particular subclass of interest is stochastic monotone binary systems (SMBS), which are characterized by nondecreasing structure. We explore the combinatorics of SBS, which provide building blocks for system reliability estimation, looking at minimal nonoperational subsystems, called mincuts. One key concept to understand the underlying combinatorics of SBS is duality. As methods for exact evaluation take exponential time, we discuss the use of Monte Carlo algorithms. In particular, we discuss the F‐Monte Carlo method for estimating the reliability polynomial for homogeneous SBS, the recursive variance reduction for SMBS, which builds upon the efficient determination of mincuts, and three additional methods that combine in different ways the well‐known techniques of permutation Monte Carlo and splitting. These last three methods are based on a stochastic process called the creation process, a temporal evolution of the SBS which is static by definition. All the methods are compared using different topologies, showing large efficiency gains over the basic Monte Carlo scheme.

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The Creation and the Destruction Processes (CP and DP) are the basis of many efficient Monte Carlo methods for estimating the unreliability of highly reliable networks on both, the static and the stochastic flow network models, for the case of independent components. Some of these methods are based on the Splitting variance reduction techniques. Due to the Splitting basic mechanism, they operate over CP. Here we propose a Splittingbased Monte Carlo method, using the Marshall-Olkin copula for the case of non independent components. This proposal operates on the DP, because the Marshall-Olkin copula model over networks is quite related -and somehow similar-to DP, which is unusual but here necessary. Before addressing the proposal, the article presents a review of the methods based on CP and DP. At the end, a comparative experimental analysis shows the efficiency of the proposed approach.