To maintain a stable stack temperature in marine fuel cell systems, the stack cooling system can be configured by appropriately combining a closed-loop fresh water line and an open-loop seawater line. The heat exchange between the fresh water and seawater is determined by the degree of opening of a three-way valve installed in the stack cooling system. The relationship between the discharge flow rates of the fresh water and seawater lines, and the degree of opening of the three-way valve, is not clearly defined, as it exhibits a complex behavior due to its operation in conjunction with the fuel cell stack. In this study, statistical techniques were applied to interpret the relationship between the components of the cooling system and fuel cell stack, when operated together. A 30-kW class PEMFC system was modeled with fresh water and seawater lines to obtain the necessary data, and simulations were conducted under various conditions. Parameters, such as the degree of opening of the three-way valve, system efficiency, and dynamic responsiveness, derived from scenarios involving variations in the pump discharge flow, load conditions, etc., were visualized using statistical techniques, including axis redefinition and normalization. The proposed approach allows for clear visualization of the relationships among various pieces of equipment through visual data and enables prediction of system efficiency, power consumption, and normal operation of the system when the operating conditions are altered beforehand. Furthermore, this study serves as a foundational research defining the characteristics of complex systems, and paves the way for potential advancements in handling big data in marine research.