Evaluating the robustness of critical infrastructure is important for good decisions and for communicating progress toward greater robustness. Nonetheless there is no widely accepted measure analogous to readily available measures of cost-efficiency; our aim here is to examine the usefulness of some candidate robustness measures. A number of possible choices can be computed based on different principles including network topology, entropy and direct estimation of cumulative maximum capacity loss, and measures based on the latter principles are suggested here. To judge their usefulness we introduce the required-capacity survival function and compute this function on representations of four electrical grids, together with a set of scalar robustness measures, conditional on publicly available information. We then evaluate the degree to which the scalar measures provide adequate summary indicators of the more comprehensive capacity-loss information revealed in the survival functions. The measures produce substantially different results, and we find in particular that topological measures correspond only weakly with cumulative capacity loss from destructive events.

评估关键基础架构的健壮性对于做出明智的决策以及传达实现更大健壮性的进展至关重要。然而，没有类似于现成的成本效率措施的广泛接受的措施。我们的目的是研究某些候选鲁棒性度量的有用性。可以基于不同的原理（包括网络拓扑，熵和累积最大容量损失的直接估计）来计算许多可能的选择，并在此建议基于后一种原理的措施。为了判断其有效性，我们引入了所需容量的生存函数，并根据四个电网的表示以及一组标量鲁棒性度量（以公开信息为条件）对该函数进行计算。然后，我们评估标量度量为生存功能中显示的更全面的容量损失信息提供足够的摘要指标的程度。这些措施产生的结果大不相同，我们尤其发现，拓扑措施仅与破坏性事件造成的累积容量损失相对应。