Recent advances in the manufacturing industry have enabled the deployment of Cyber-Physical Systems (CPS) at scale. By utilizing advanced analytics, data from production can be analyzed and used to monitor and improve the process and product quality. Many frameworks for implementing CPS have been developed to structure the relationship between the digital and the physical worlds. However, there is no systematic review of the existing frameworks related to quality management in manufacturing CPS. Thus, our study aims at determining and comparing the existing frameworks. The systematic review yielded 38 frameworks analyzed regarding their characteristics, use of data science and Machine Learning (ML), and shortcomings and open research issues. The identified issues mainly relate to limitations in cross-industry/cross-process applicability, the use of ML, big data handling, and data security.