In the context of industrially mass-manufactured products, quality management is based on physically inspecting a small sample from a large batch and reasoning about the batch's quality conformance. When complementing physical inspections with predictions from machine learning models, it is crucial that the uncertainty of the prediction is known. Otherwise, the application of established quality management concepts is not legitimate. Deterministic (machine learning) models lack quantification of their predictive uncertainty and are therefore unsuitable. Probabilistic (machine learning) models provide a predictive uncertainty along with the prediction. However, a concise relationship is missing between the measurement uncertainty of physical inspections and the predictive uncertainty of probabilistic models in their application in quality management. Here, we show how the predictive uncertainty of probabilistic (machine learning) models is related to the measurement uncertainty of physical inspections. This enables the use of probabilistic models for virtual inspections and integrates them into existing quality management concepts. Thus, we can provide a virtual measurement for any quality characteristic based on the process data and achieve a 100 percent inspection rate. In the field of Predictive Quality, the virtual measurement is of great interest. Based on our results, physical inspections with a low sampling rate can be accompanied by virtual measurements that allow an inspection rate of 100 percent. We add substantial value, especially to complex process chains, as faulty products/parts are identified promptly and upcoming process steps can be aborted.

翻译：在工业批量生产产品的背景下，质量管理基于从大批量中抽取小样本进行物理检测，并推断该批次的质量符合性。当用机器学习模型的预测结果补充物理检测时，关键在于预测的不确定性必须是已知的——否则，既有的质量管理概念便无法合法应用。确定性（机器学习）模型缺乏对其预测不确定性的量化，因此不适用。概率性（机器学习）模型在提供预测结果的同时还能给出预测不确定性。然而，在质量管理应用中，物理检测的测量不确定性与概率性模型的预测不确定性之间尚缺乏明确的对应关系。本文阐述了概率性（机器学习）模型的预测不确定性如何与物理检测的测量不确定性相关联。这使得概率性模型可用于虚拟检测，并将其融入现有的质量管理体系中。由此，我们能够基于过程数据为任何质量特性提供虚拟测量，实现100%的检测覆盖率。在预测性质量领域，虚拟测量具有极大的价值。基于我们的结果，低采样率的物理检测可辅以虚拟测量，从而实现100%的检测覆盖率。这对于复杂过程链尤为有价值，因为故障产品/部件能被及时识别，后续工艺步骤也可被终止。