The complexity and non-linear interactions involved in maritime accidents make it challenging to apply traditional models of risk analysis to them. Resilience is adopting a perspective focuses on holistic aspects of safety across the pre-accident, mid-accident, and post-accident phases. This paper proposes a framework for process risk analysis of maritime accidents based on resilience theory by applying the function resonance analysis method (FRAM). We first identify a three-layer maritime accident based on maritime accident investigation reports and then analyze the potential variability of all relevant functions. Subsequently, a FRAM model is constructed to analyze the accident's functional resonance of accidents by aggregating variations in the functions. Finally, we apply Monte Carlo simulations to compute the values of coupling of all interconnected functions. The ship grounding accidents in Arctic waters is chosen as the case to demonstrate the proposed framework. The relationships of influence between the functions were analyzed to obtain critical coupling pathways of coupling between them, and a time-weighted PageRank algorithm was used to identify key functions. The results show that the proposed approach can reveal vulnerabilities and instabilities in the system, and enables the proposal of targeted, long-term measures of risk control to enhance its resilience and safety.