Implementation of the calibration’s VIM3 definition using the matrix of variance–covariance of input data
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This paper discusses the effects following the implementation of the concept of calibration presented in the 3rd edition of the international vocabulary of metrology—basic and general concepts and associated terms (VIM) and the repercussions of practitioners adopting VIM3. The new definition leads to modifications in the treatment of calibration data. It is now necessary to establish a relation which allows obtaining any measurement result from any indication of the measuring instrument. This relation takes into account uncertainties and any covariances, both on the values of the standards used and on the indications and maybe even the covariances. The usual statistical technique of regression, the ordinary least squares adjustment, does not generally enable to reach this goal. As a result, more sophisticated methods need to be used, for instance the Generalised Gauss Markov Regression. We compared both methods on a gas chromatograph calibration example.
KeywordsCalibration Metrological terminology VIM Ordinary least squares (OLS) Generalised Gauss Markov Regression (GGMR) Measurement uncertainty Variance–covariance matrix
This article is based on the discussions in the working group of the College Français de Métrologie, and the authors thank all the participants for the fruitful discussions . Many thanks to Béatrice Lalère and Adrien Caurant for providing data related to the example of gas chromatograph calibration. The treatment of data presented in the example is based on software developed by a statistical project team leaded by Catherine Yardin from LNE.
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