Measurement Uncertainty: Relating the uncertainties of physical and
  virtual measurements
Simon Cramer Tobias Müller Robert H. Schmitt
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.