Creating reliable and robust quality control systems that identify process errors while having a low number of false rejects is a considerable challenge in the automated manufacturing industry. Especially in the pharmaceutical industry, where a product's quality has to be ensured at all costs, a large amount of false rejects is acceptable to guarantee the integrity of all released products. As standard quality control systems mainly perform a binary classification, most of them do not provide insights about the reason behind rejections. As a result, the underlying reason for the rejects, such as degradation in equipment or wrong settings in process parameters, often goes unnoticed. Yet, these systems are based on conservative approaches that incorporate the uncertainties related to the measurement system and process variation such as batch-to-batch variations and assembly tolerances. In this contribution, a new data-driven quality control system is suggested. The system is based on well-established machine learning methods that differentiate multiple types of errors in the assembly processes of medical products. Trained on process data, the system's functionality is demonstrated in a pre-study and two real industrial use cases. Moreover, application-specific differences are discussed. It is shown that for the two use cases and a limited number of batches the system not only detects 100% of all defective products but also limits the number of false rejects to an acceptable amount. In all of the application examples, the system has the potential to be executed as a soft real-time system that allows integration into industrial processes. Moreover, it is shown that the algorithm can present the extracted knowledge in various forms understandable for humans, allowing for more informed decision making.