This study formulates and analyzes a decision-making optimization problem for emergency response actions at nuclear power plants using Probabilistic Risk Assessment (PRA). Taking the replenishment of multiple water tanks by fire trucks as a case study, we apply multi-objective Pareto optimization to determine the optimal intervention threshold θ — the water level at which switching operations should be triggered — with the objective of simultaneously minimizing failure probability and personnel resource requirements.
Operational time uncertainty is introduced as a stochastic variable parameterized by standard deviation σ, and three cases (σ = 0.0, 0.5, and 1.0 hours) are systematically analyzed. Results demonstrate that explicitly incorporating uncertainty into the optimization yields decision-relevant insights that go beyond single-point estimates: the Pareto-optimal threshold shifts substantially with σ, and failure probabilities improve by up to 66% when uncertainty-aware thresholds are applied instead of deterministic ones.
Furthermore, we apply the Expected Value of Including Uncertainty (EVIU) to quantify the economic value of reducing uncertainty through training, standardization, or data acquisition. The analysis shows that reducing variability (σ) in operation time can substantially decrease failure probability and decision loss, justifying investments in training and procedural improvements.