A composite metric for evaluating system resilience with non-idealistic performance curves

Designing systems and processes resilient to sudden shocks is an essential element of system analysis in many engineering fields. Quantitative resilience assessment employs various metrics to examine and monitor system resilience through experimentation. Existing resilience metrics typically portray the system's response to a shock-like event as an inverse bell-shaped, triangular, or trapezoidal curve of performance over time. Then, for example, the downward and upward slopes are interpreted as the disruption and restoration phases of the system, respectively. However, these metrics fail or need simplification when a system response does not exhibit such an idealized shape. In this paper, we introduce a composite metric combining various elements of system performance curves, irrespective of shape features. Additionally, the metric integrates a user-defined critical threshold into its mathematical formulation. To verify the metric's performance, we conducted a survey among researchers in energy system analysis using illustrative system response curves. Comparing the survey-derived ranking and the metric values verifies that the metric aligns with the judgment and expectations of potential users. Finally, we benchmark our metric against its contemporaries, highlighting its versatility with nontypical performance curves. Due to its modular mathematical formulation, this metric can be applied, enhanced, and extended for comparative performance assessment in various fields of analysis, especially in the absence of idealized system response curves.