On the reliability estimation of stochastic binary systems

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