The Effect of Time-Varying Value on Infrastructure Resilience Assessments

Infrastructure resilience for a scenario can be assessed quantitatively from resilience curves that plot the evolution of system performance. Summary metrics map these curves to a single value to facilitate comparisons of different systems, scenarios, and policies. Commonly, these metrics are integral-based, e.g., cumulative infrastructure performance. However, since these curves and metrics only examine infrastructure performance, they fail to consider the dynamics of when stakeholders value the performance. For example, a power failure at a hospital during an ordinary day would be of less concern to emergency managers than during a hurricane recovery. This manuscript defines value weighting functions to represent the evolution of stakeholders’ value of performance. Temporal correlation between the performance and value weighting functions is described through a stochastic offset. Together, these concepts are used to define a holistic resilience metric: percent value satisfied. Through analytical and numerical approaches, percent value satisfied is treated as a resilience assessment’s stochastic output, and its distribution is compared to the naïve metric, cumulative infrastructure performance. The naïve summary metric is shown to be misleading in multiple potential scenarios; this work establishes that resilience assessments must consider the impact of time-varying stakeholder value and its correlation with infrastructure performance. These elements also provide new considerations for resilience assessments: opportunities to improve holistic system resilience without directly affecting infrastructure performance; hazard categories to inform value-weighted resilience analysis; and general insights to guide extensions from performance-based to value-weighted assessment.