Decomposition of general facility disruption correlations via augmentation of virtual supporting stations

Infrastructure facilities may be subject to probabilistic disruptions that compromise individual facility functionality as well as overall system performance. Disruptions of distributed facilities often exhibit complex spatial correlations, and thus it is difficult to describe them with succinct mathematical models. This paper proposes a new methodological framework for analyzing and modeling facility disruptions with general correlations. This framework first proposes pairwise transformations that unify three probabilistic representations (i.e., based on conditional, marginal, and scenario probabilities) of generally correlated disruption profile among multiple distributed facilities. Then facilities with any of these disruption profile representations can be augmented into an equivalent network structure consisting of additional supporting stations that experience only independent failures. This decomposition scheme largely reduces the complexity associated with system evaluation and optimization. We prove analytical properties of the transformations and the decomposition scheme, and illustrate the proposed methodological framework using a set of numerical case studies and sensitivity analyses. Managerial insights are also drawn.