Predictive Resilience Modeling Using Statistical Regression Methods

Abstract

Resilience describes the capacity of systems to react to, withstand, adjust to, and recover from disruptive events. Despite numerous metrics proposed to quantify resilience, few studies predict these metrics or the restoration time to nominal performance levels, and these studies often focus on a single domain. This paper introduces three methods to model system performance and resilience metrics, which are applicable to various engineering and social science domains. These models utilize reliability engineering techniques, including bathtub-shaped functions, mixture distributions, and regression analysis incorporating event intensity covariates. Historical U.S. job loss data during recessions are used to evaluate these approaches’ predictive accuracy. This study computes goodness-of-fit measures, confidence intervals, and resilience metrics. The results show that bathtub-shaped functions and mixture distributions accurately predict curves possessing V, U, L, and J shapes but struggle with W and K shapes involving multiple disruptions or sudden performance drops. In contrast, covariate-based models effectively track all curve types, including complex W and K shapes, like the successive shocks in the 1980 U.S. recession and the sharp decline in the 2020 U.S. recession. These models achieve a high predictive accuracy for future performance and resilience metrics, evidenced by the low sum of square errors and high adjusted coefficients of determination.