Abstract
Resilience is the ability of a system to respond, absorb, adapt, and recover from a disruptive event, finding applications in diverse domains. Previous research focused on resilience models not designed to predict multiple disruptions and recoveries, resilience metrics typically calculated after disruptions, optimal allocation strategies that are domain-dependent and focus on internal components, and maintenance scheduling. These approaches enable retrospective analysis to assess how well the system performed under stress and inform future design and operational decisions, but do not project when the system will recover toa specified level of performance or what actions to take in order to reach a target level of performance quickly and cost effectively. Without predictive models, emergency management teams tasked with making critical decisions at times of intense stress will struggle to optimally respond to disruptive scenarios that may impact the lives of thousands or millions of individuals. To address the limitation of past research, this dissertation develops predictive resilience models that leverage advanced statistical techniques from regression and time series analysis to forecast system performance and support decision-making processes aimed at enhancing system resilience. These models possess a level of mathematical abstraction that is general and may be applied to different domains to which resilience is relevant. The general model developed in this dissertation enhances the resilience engineering field with the capability of characterizing a variety of systems possessing multiple shocks and recurrent recoveries that can (i) track and predict a primary event followed by a chain of consequences that can be moderate or more severe than the first disruption, (ii) help emergency management teams tasked with making critical decisions at times of intense stress to optimally respond to those disruptive scenarios that may impact the lives of thousands or millions of individuals, and(iii) assess to which level resilience engineering is relevant to a system. These models are validated using diverse datasets, including economic, cybersecurity, and a simulated radar system data, in order to demonstrate the applicability of these models to different domains. Goodness-of-fit measures, confidence intervals, and resilience metrics are computed to asses show well the models perform on the data sets considered. The results suggest that although simpler statistical models are suitable for modeling and prediction of some resilience curves, mixture models are much more flexible and achieve greater predictive accuracy. Moreover, optimal allocation strategies developed in this dissertation efficiently distribute limited resources among the covariates associated with restoration activities. These strategies achieved targeted system performance goals within budget constraints, enhancing the resilience of systems.