Abstract
A virtual experiment simulates a real measurement process by means of a numerical model. The numerical model produces virtual data whose properties reflect those of the data observed in the real experiment. In this work, we explore how the results of a virtual experiment can be employed in the context of uncertainty evaluation for a corresponding real experiment. The uncertainty evaluation was based on the Guide to the Expression of Uncertainty in Measurement (GUM), which defines the de facto standard for uncertainty evaluation in metrology. We show that, under specific assumptions about model structure and variance of the data, virtual experiments in combination with a Monte Carlo method lead to an uncertainty evaluation for the real experiment that is in line with Supplement 1 to the GUM. In the general case, a GUM-compliant uncertainty evaluation in the context of a real experiment can no longer be based on a corresponding virtual experiment in a simple way. Nevertheless, virtual experiments are still useful in order to increase the reliability of an uncertainty analysis. Simple generic examples as well the case study of a virtual coordinate measuring machine are presented to illustrate the treatment.
Highlights
A virtual experiment is a numerical model of an experiment or a measurement process [1]
For a linear relationship that typically arises in direct measurements, the results of the virtual experiment can be immediately used for a GUM-compliant uncertainty evaluation, provided that the variance of the distribution of the real data is known with sufficient accuracy
We show that, for linear models and known variance of the distribution of observations in the real experiment, a Monte Carlo procedure applied to the virtual experiment produces samples that equal those of the GUM-S1 Monte Carlo uncertainty evaluation
Summary
A virtual experiment is a numerical model of an experiment or a measurement process [1]. Even when the experiment aims at a direct measurement of the measurand, proper inference of the measurand usually requires the application of an analysis model that contains additional correction terms In these cases, the analysis model plays a different role than the numerical model of the virtual experiment. The GUM uncertainty framework is based on a measurement model that determines the measurand as a function of its input quantities, and the data observed in the real experiment typically represent one of these input quantities. Supplements 1 (GUM-S1) [16] and 2 (GUM-S2) [17] recommend a Monte Carlo method for uncertainty evaluation that propagates probability density functions (PDFs) characterizing one’s state of knowledge about the input quantities through the GUM measurement model in order to determine the PDF for the measurand.
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