As engineered systems expand, become more interdependent, and operate in real-time, reliability assessment is key to inform investment and decision making. However, network reliability problems are known to be #P-complete, a computational complexity class believed to be intractable, and thus motivate the quest for approximations. Based on their theoretical foundations, reliability evaluation methods can be grouped as: (i) exact or bounds, (ii) guarantee-less sampling, and (iii) probably approximately correct (PAC). Group (i) is well regarded due to its useful byproducts, but it does not scale in practice. Group (ii) scales well and verifies desirable properties, such as the bounded relative error, but it lacks error guarantees. Group (iii) is of great interest when precision and scalability are required. We introduce K-RelNet, an extended counting-based method that delivers PAC guarantees for the K-terminal reliability problem. We also put our developments in context relative to classical and emerging techniques to facilitate dissemination. Then, we test in a fair way the performance of competitive methods using various benchmark systems. We note the range of application of algorithms and suggest a foundation for future computational reliability and resilience engineering, given the need for principled uncertainty quantification in complex systems. and K ⊆ V is the set of terminals. We let G(P) be a stochastic graph, where every edge e ∈ E vanishes from G with respective probabilities P = (p e ) e∈E . We assume a binary-system, and say G(P) is unsafe if a subset of vertices in K becomes disconnected, and safe otherwise. Thus, given instance (G, P) of the K-terminal reliability problem, we are interested in computing the unreliability of G(P), denoted u G (P), and defined as the probability that G(P) is unsafe.If |Θ| is the cardinality of set Θ, then n = |V| and m = |E| are the number of vertices and edges, respectively. Also, when |K| = n and |K| = 2, the K-terminal reliability problem reduces to the all-terminal and two-terminal reliability problems, respectively. These are well-known and proven to be #P-complete problems [1,2]. The more general K-terminal reliability problem is #P-hard, so ongoing efforts to compute u G (P) focus on practical bounds and approximations.Exact and bounding methods are limited to networks of small size, or with bounded graph properties such as treewidth and diameter [3,4]. Thus, for large G of general structure, researchers and practitioners lean on simulation-based estimates with acceptable Monte Carlo error [5]. However, in the absence of an error prescription, simulation applications can use unjustified sample sizes and lack a priori rigor on the quality of the estimates, thus becoming guarantee-less methods.A formal approach to guarantee quality in Monte Carlo applications relies on the so-called ( , δ) approximations, where and δ are user specified parameters regarding the relative error and confidence, respectively. As an illustration, for Y as a random variable (RV), say we ...

Modern society is increasingly reliant on the functionality of infrastructure facilities and utility services. Consequently, there has been surge of interest in the problem of quantification of system reliability, which is known to be #P-complete. Reliability also contributes to the resilience of systems, so as to effectively make them bounce back after contingencies. Despite diverse progress, most techniques to estimate system reliability and resilience remain computationally expensive. In this paper, we investigate how recent advances in hashing-based approaches to counting can be exploited to improve computational techniques for system reliability.The primary contribution of this paper is a novel framework, RelNet, that reduces the problem of computing reliability for a given network to counting the number of satisfying assignments of a Σ11 formula, which is amenable to recent hashing-based techniques developed for counting satisfying assignments of SAT formula. We then apply RelNet to ten real world power-transmission grids across different cities in the U.S. and are able to obtain, to the best of our knowledge, the first theoretically sound a priori estimates of reliability between several pairs of nodes of interest. Such estimates will help managing uncertainty and support rational decision making for community resilience.

Summary Reliability and risk assessment of lifeline systems call for efficient methods that integrate hazard and interdependencies. Such methods are computationally challenged when the probabilistic response of systems is tied to multiple events, as performance quantification requires a large catalog of ground motions. Available methods to address this issue use catalog reductions and importance sampling. However, besides comparisons against baseline Monte Carlo trials in select cases, there is no guarantee that such methods will perform or scale well in practice. This paper proposes a new efficient method for reliability assessment of interdependent lifeline systems, termed RAILS, that considers systemic performance and is particularly effective when dealing with large catalogs of events. RAILS uses the state‐space partition method to estimate systemic reliability with theoretical bounds and, for the first time, supports cyclic interdependencies among lifeline systems. Recycling computations across an entire seismic catalog with RAILS considerably reduces the number of system performance evaluations in seismic performance studies. Also, when performance estimate bounds are not tight, we adopt an importance and stratified sampling method that in our computational experiments is various orders of magnitude more efficient than crude Monte Carlo. We assess the efficiency of RAILS using synthetic networks and illustrate its application to quantify the seismic risk of realistic yet streamlined systems hypothetically located in the San Francisco Bay Region.

No abstract