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Infrastructure networks, such as electrical power grids, transportation and water supply systems, support critical societal functions of society. Failures of such networks can have severe consequences, and quantification of the probability of failure of such systems is essential for understanding and managing their reliability. Analytical and simulation methods have been proposed to solve such kinds of problems, among which sampling methods feature prominently. Recently, the authors extended widely used structural reliability algorithms, subset simulation, cross-entropy-based importance sampling as well as uncertainty quantification methods built from particle integration methods and exact confidence, all for efficient reliability analysis in discrete spaces. This paper tests the performance of these algorithms for static network reliability assessment. In particular, we compare these methods for optimal power flow problems in various IEEE benchmark models. Overall, the cross-entropy-based method outperforms the other methods in all benchmark models except the largest IEEE 300, while the adaptive effort subset simulation and particle integration methods are more suitable for handling high-dimensional problems. By building up the benchmark models, we provide unified examples for comparing different emerging methods in static network reliability assessment and also to support improvement or combination of these methods. 

Infrastructure networks offer critical services to modern society. They dynamically interact with the environment, operators, and users. Infrastructure networks are unique engineered systems, large in scale and high in complexity. One fundamental issue for their reliability assessment is the uncertainty propagation from stochastic disturbances across interconnected components. Monte Carlo simulation (MCS) remains approachable to quantify stochastic dynamics from components to systems. Its application depends on time efficiency along with the capability of delivering reliable approximations. In this paper, we introduce Quasi Monte Carlo (QMC) sampling techniques to improve modeling efficiency. Also, we suggest a principled Monte Carlo (PMC) method that equips the crude MCS with Probably Approximately Correct (PAC) approaches to deliver guaranteed approximations. We compare our proposed schemes with a competitive approach for stochastic dynamic analysis, namely the Probability Density Evolution Method (PDEM). Our computational experiments are on ideal but complex enough source-terminal (S-T) dynamic network reliability problems. We endow network links with oscillators so that they can jump across safe and failed states allowing us to treat the problem from a stochastic process perspective. We find that QMC alone can yield practical accuracy, and PMC with a PAC algorithm can deliver accuracy guarantees. Also, QMC is more versatile and efficient than the PDEM for network reliability assessment. The QMC and PMC methods provide advanced uncertainty propagation techniques to support decision makers with their reliability problems.