Measurement Uncertainty: Relating the uncertainties of physical and virtual measurements

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.