Impact of Imperfect Artefacts and the Modus Operandi on Uncertainty Quantification Using Virtual Instruments

Abstract

The usage of virtual instruments (VIs) to analyze measurements and calculate uncertainties is increasing. Well-known examples are virtual coordinate measurement machines (VCMMs) which are often used and even commercially offered to assess measurement uncertainties of CMMs. A more recent usage of the VI concept is posed by the modeling of scatterometers. These VIs can be used to assess the measurement uncertainty after the measurement has been performed based on the real measurement data or prior to the measurement to predict the measurement uncertainty using a type of simulated measurement data. The research question addressed in this paper is to assess if this predicted uncertainty will be similar in magnitude to the calculated uncertainty based on the measurement data. It turns out that this is not necessarily the case. The main observation of this paper was that the uncertainty predicted by a VI can be highly sensitive to the chosen way of operating the VI. To amend this situation, a simple procedure was proposed that can be used prior to performing the real measurement and that is believed to produce a conservative prediction of the measurement uncertainty in most cases. This was verified in a case study involving the measurement of the asphericity of an imperfect sphere using a CMM, with the uncertainty calculated by means of a VCMM.

D2.4 - On Uncertainty Evaluation using Virtual Experiments

“…While the GUM (and GUM S1) uncertainty evaluation follows rather strict rules this is not the case when applying Monte-Carlo to a virtual experiment. In fact, a Monte-Carlo virtual experiment can be carried out following rather different strategies which may even lead to markedly different resulting uncertainties as demonstrated in [4].…”

Virtual experiments for the assessment of data analysis and uncertainty quantification methods in scatterometry

“…Virtual experiments provide a numerical model for real measurements and they are used, for example, to identify relevant sources of uncertainty [1,10], to specify tolerances required for reaching a desired accuracy [9] or for the design of novel measurement principles. Virtual experiments have also been applied for uncertainty quantification, particularly when combined with Monte Carlo methods, see [3,[11][12][13][14][15]. Specifically for complex measurement setups, virtual experiments can be vital to quantitatively explore the impact of all influencing quantities, and carrying out a sensitivity analysis in silico is in many cases the only way to design or improve modern complex measurement devices.…”