LNG serves as a pivotal element within integrated energy systems, especially in coastal regions where the implementation of a stable and reliable LNG cold energy power generation system significantly elevates energy efficiency. This system can effectively meet concurrent demands for cold energy utilization and electricity supply while contributing to the mitigation of carbon emissions. However, the inherent complexity of the system coupled with the scarcity of historical operational data for the novel dual-Rankine cycle process renders conventional reliability assessment methodologies inadequate. This study proposes an integrated framework utilizing fuzzy Bayesian methods to address data scarcity during the early stages of equipment deployment. A hierarchical risk factor model, incorporating process decomposition, expert evaluations, and triangular fuzzy numbers, is developed to quantify uncertainties in failure probabilities. The Bayesian network models the causal relationships among equipment failure factors, allowing for the inference of overall system reliability from individual equipment performance. Through a case study of a LNG terminal in Zhoushan, this approach integrates sensitivity analysis with forward-backward reasoning methodologies to rigorously evaluate and quantify system reliability under operational conditions. The results show that under high load conditions within the 1000 h prior to overhaul, following long-term accumulated operation, the probability of complete system shutdown in the power generation system is 3.30%, while the probability of the LNG cold energy power generation system failing to operate fully due to aging-related faults is 8.24%, demonstrating the system’s strong reliability under extreme conditions. Critical risks identified through backward inference include the seawater pump SWP1, with a posterior failure probability of 59.92% during complete shutdown, and the propane-side pump SWP3, with a posterior failure probability of 32.29% when the cold energy power generation system can only operate in a single-cycle mode. This study provides an advanced methodological framework for risk management in newly constructed LNG cold energy power generation systems, playing a crucial role in promoting sustainable, low-carbon technologies in the energy sector.