The lack of information on the correlation between root causes and corresponding control criteria in the importance calculation of root causes of design problems results in less accurate determinations of core problems. Based on the interaction between customer needs, bad product parameters, and root causes, a hierarchical representation model of the design problem is established in this paper. A network layer of bad parameters, including various types of correlations, and a control layer, including technical feasibility and cost, are constructed. Then, a method based on the network analytic hierarchy process is proposed to rank the importance of root causes of the design problem and determine the core problems. Finally, a product design process based on the core problem solving is established to assist designers with improving design quality and efficiency. The design for the coolant flow distribution device in the lower chamber of a third-generation pressurized water reactor is employed as an example to demonstrate the effectiveness of the proposed method.