Manufacturing environments are characterized by non-stationary processes, constantly varying conditions, complex process interdependencies, and a high number of product variants. These and other aspects pose several challenges for common machine learning algorithms to achieve reliable and accurate predictions. This overview and vision paper provides a comprehensive list of common problems and challenges for data science approaches to quality control in manufacturing. We have derived these problems and challenges by inspecting three real-world use cases in the eld of product quality control and via a comprehensive literature study. We furthermore associate the identi ed problems and challenges to individual layers and components of a functional setup, as it can be found in manufacturing environments today. Additionally, we extend and revise this functional setup and this way propose our vision of a future functional software architecture. This functional architecture represents a visionary blueprint for solutions that are able to address all challenges for data science approaches in manufacturing quality control.