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.
Afolabi et al. (Thu,) studied this question.