Robust Scenario-Based Sufficiency Assessment of Multi-Layer Physical Protection Systems

Introduction. Evaluating the effectiveness of multi-layer physical protection systems by average performance alone may conceal inadequate protection under adverse operational conditions. For special-purpose facilities and critical infrastructure, the coordination of detection, delay and response functions requires an explicit measure of time sufficiency. A scenario-conditioned probability of a safe state is formulated as the product of detection probability, timely response probability and conditional intervention success. Delay and response times are represented by independent normal variables within three synthetic operating scenarios. Eighteen discrete resource configurations are evaluated by exact probability calculations and independently checked by Monte Carlo simulation. Two decision criteria are compared: a minimum scenario-weighted mean and a joint mean and worst-scenario requirement. Materials and Methods. A widely used representation of system effectiveness multiplies the probability of detection, the probability of timely response, and the conditional probability of successful intervention. Its usefulness depends on how the conditional factors are defined. In particular, replacing uncertain times with their mean values can conceal the probability that response is delayed beyond the available protection interval. Moreover, a weighted average across scenarios may remain acceptable even when the most demanding scenario is insufficiently protected. The present work therefore distinguishes statistical performance evaluation from a decision requirement applied to every considered scenario. Results. The experiment shows why a mean effectiveness requirement cannot replace a worst-scenario sufficiency condition. The average-only solution satisfies a probability threshold of 0.75 at a cost of 9 arbitrary units, but its worst-scenario performance is 0.4939. Adding the requirement of at least 0.60 in every scenario yields a least-cost alternative of 13 units, with a mean probability of 0.8111 and a worst-scenario value of 0.6156. Conclusions. A scenario-based chance-constrained method has been developed for evaluating functional sufficiency in multi-layer physical protection systems. It connects detection, stochastic time sufficiency and conditional intervention success to a measurable probability of a safe state. The model is applicable as a conceptual decision-support framework for special-purpose facilities and critical infrastructure, without assuming the same threat profile for these distinct facility categories.