To prevent accidents such as collisions, fires, and explosions during ship operations, a functional resonance analysis method （FRAM） that integrates subjective and objective factors is proposed and employed to analyze the safety of ship missions and identify potential resonant links.

First, hierarchical task analysis （HTA） is employed to determine the main functions of the task. Next, the output variability of each function is calculated using the interval-valued hesitant fuzzy weighted average （IVHFWA） operator and Euclidean distance. The FP-growth algorithm is then employed to mine the association rules of upstream and downstream functions in accident cases, and the variability of function coupling is calculated based on the lift. Finally, based on the coupling variability scores, key functions and links that are prone to functional resonance in the system are identified, and corresponding barrier measures are established for focused monitoring.

Taking the safety analysis of a submarine far-sea training mission as an example, the results indicate the existence of two critical links that generate functional resonance and may lead to accidents.

The results of this study can provide vital decision-making support to ensure the safety of ship's missions.