Quantitative assessment of crises via central moments

We provide a widely applicable method to quantitatively assess the response of socio-technical systems to crises. The method generalizes the interpretability of a series of moments in terms of probability distributions to the breakdown and recovery phases of crises. These moments allow to unveil subtle differences in the reactions of distinct systems in view of a crisis, and, in part, serve as a measure of these systems’ resilience. Thereby, the moments extend existing measures of resilience by a well-defined procedure regarding the time domain that extracts relevant time scales of the systems’ reaction to a given crisis during breakdown and recovery. The method is illustrated by real-world data of German airports which experienced a dramatic drop in flight departures as a consequence of travel restrictions imposed in connection with the COVID-19 pandemic.