A Reliability-Centred Statistical Framework for Resilience Quantification and Investment Optimization of Energy Infrastructure under Uncertainty

Energy infrastructure systems are increasingly exposed to uncertainty arising from aging assets, environmental hazards, and operational volatility. This study presents a hybrid reliability-centred statistical framework for quantifying and optimizing the resilience of energy systems, integrating Weibull reliability modelling, Monte Carlo uncertainty analysis, and cost–resilience trade-off optimization. Synthetic failure-time data were simulated using a Weibull distribution (β = 1.8, η = 5000 hr) to represent realistic component degradation patterns. The system resilience index (R) was computed from performance recovery profiles, while uncertainty propagation was analyzed through probabilistic reliability simulations. A Particle Swarm Optimization (PSO) algorithm was then employed to determine the optimal investment level balancing resilience improvement and maintenance cost. Results indicate that moderate investment (~6.8 units) achieves the best trade-off between cost and system resilience (R = 0.82), with Monte Carlo reliability 95% CI of [0.78, 0.92], revealing the influence of stochastic failure behaviour. The proposed framework provides a decision-support tool for policymakers and system engineers to prioritize resource allocation, enhance adaptive capacity, and maintain operational reliability in uncertain environments.