Due to the energy crisis, ammonia stands out as an efficient hydrogen energy carrier. However, liquid ammonia's nature of toxicity, corrosiveness, volatility, flammability, etc., make its storage highly risky. It is essential to analyze the risk of the ammonia storage facility for its safety improvement. Failure mode and effect analysis (FMEA) has been a popular risk analysis method due to its ease of implementation. However, traditional FMEA is insufficient to model the uncertainty of risk assessment information, enhance the consensus among experts, aggregate experts' risk evaluation information, and derive reliable risk analysis results. To address these limitations, we introduce a hybrid probabilistic linguistic FMEA framework to analyze failure risk in the ammonia storage facility. First, the probabilistic linguistic terms (PLTs) are introduced to express uncertain risk evaluation information of failure modes. Second, a risk acceptability-based consensus-reaching process is introduced to measure experts' consensus on each failure mode's risk and improve their consensus. Then, a consensus degree-based ordered weighted averaging operator is introduced to fuse experts' risk evaluation information, where experts' weight is determined by their consensus degree. Furthermore, the gained and lost dominance score method is improved on the basis of the expected value of the PLTs to prioritize failure modes' risk. Finally, a case study of the risk analysis for the ammonia storage facility is performed to show the efficiency of the extended FMEA. The case study indicated that condenser cooling water pump failure and failure of level transfer are the top two failure modes and have risk scores of 0.126 and 0.091, respectively.