A Probabilistic Framework for Detection Performance of Periodically Sampled Hazard Monitoring Systems: Application to Electric Shock Drowning Risk Reduction

This paper presents a general probabilistic framework for evaluating secondary-outcome risk when primary events occur randomly and are monitored by a periodically sampled detection system. The model combines primary-event occurrence, temporal and non-temporal detection failures, response effectiveness, and the conditional probability of a secondary outcome. Primary events are modeled using a Poisson process. Closed-form expressions are developed for temporal detection and miss probabilities, the effective per-event probability of a secondary outcome, the probability of at least one secondary outcome during a specified observation horizon, and the expected number of secondary outcomes. Monte Carlo simulations are used to verify the analytical temporal-detection results and evaluate their sensitivity to event duration and measurement period. Electrical-shock-drowning risk in marinas is used as an illustrative application. The paper compares unmonitored and monitored conditions, including idealized timing-only detection and a generalized case incorporating non-temporal misses and imperfect response. It also introduces a Marina Safety Index and two distinct relative-risk-reduction measures: one based on the probability of at least one dangerous outcome and another based on the expected number of dangerous outcomes. The framework is intended for analytical risk evaluation, system design comparison, and sensitivity analysis. Numerical examples are illustrative and should not be interpreted as empirical estimates of the actual incidence of hazardous electrical-leakage events or human exposure at a particular marina.