Automobile manufacturers often outsource key components and parts to suppliers, hence ensuring that process quality has been a hot topic in current research. The quality control demands at different stages of the manufacturing supply chain cycle have been ignored in traditional process quality control methods. To solve this issue, this paper takes the three-cylinder engine balance shaft system as the research object, and builds a process quality control model for the three-cylinder engine balance shaft system oriented to the manufacturing supply chain. The metagraph theory is introduced, and parts suppliers in the manufacturing supply chain, product process quality attributes, supply chain revenue function, and other key elements are defined. By constructing the revenue function of the three-cylinder engine balance shaft system process quality control model, the feasibility of the proposed method is verified by taking the process quality control of one certain three-cylinder engine balance shaft system as a verification example. The results show that, with other conditions unchanged, the application of this method can increase the overall profit of the manufacturing supply chain by 100% at the stage of preparation before product machining, and more than 8% at the stage of product performance evaluation. The proposed method of process quality control based on the metagraph theory provides a theoretical basis for building an information sharing platform of product process quality, and effectively reduces the machining cost for product improvement and upgrading in the manufacturing supply chain.