The concept of negative probabilities has also been proposed for reliable facility location models where facilities are subject to negatively correlated disruption risks when facility locations, customer allocation, and backup service plans are determined simultaneously. Li et al. proposed a virtual station structure that transforms a facility network with positively correlated disruptions into an equivalent one with added virtual supporting stations, and these virtual stations were subject to independent disruptions. This approach reduces a problem from one with correlated disruptions to one without. Xie et al. later showed how negatively correlated disruptions can also be addressed by the same modeling framework, except that a virtual supporting station now may be disrupted with a “failure propensity” which