<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>We address the problem of linear comparative calibration, a special case of linear calibration where both variables are measured with errors, and the analysis of the uncertainty of the measurement results obtained with the calibrated instrument. The concept is explained in detail using the calibration experiment of the pressure transducer and the subsequent analysis of the measurement uncertainties. In this context, the calibration and the measurements with the calibrated instrument are performed according to ISO Technical Specification 28037:2010 (here referred to as ISO linear calibration), based on the approximate linear calibration model and the application of the law of propagation of uncertainty (LPU) in this approximate model. Alternatively, estimates of the calibration line parameters, their standard uncertainties, the coverage intervals and the associated probability distributions are obtained using the Monte Carlo method (MCM) based on the law of propagation of distributions (LPD). Here we also obtain the probability distributions and the coverage interval for the quantities measured with the calibrated instrument. Furthermore, motivated by the model structure of this particular example, we conducted a simulation study that presents the empirical coverage probabilities of the ISO and MCM coverage intervals and investigates the influence of the sample size, i.e. the number of calibration points in the measurement range, and the different combinations of measurement uncertainties. The study generally confirms the good properties and validity of the ISO technical specification within the considered (limited) framework of experimental designs motivated by real-world application, with small uncertainties in relation to the measurement range. We also point out the potential weaknesses of this method that require increased user attention and emphasise the need for further research in this area.</p>
</abstract>

We address the problem of linear comparative calibration, a special case of linear calibration where both variables are measured with errors, and the analysis of the uncertainty of the measurement results obtained with the calibrated instrument. The concept is explained in detail using the calibration experiment of the pressure transducer and the subsequent analysis of the measurement uncertainties. In this context, the calibration and the measurements with the calibrated instrument are performed according to ISO Technical Specification 28037:2010 (here referred to as ISO linear calibration), based on the approximate linear calibration model and the application of the law of propagation of uncertainty (LPU) in this approximate model. Alternatively, estimates of the calibration line parameters, their standard uncertainties, the coverage intervals and the associated probability distributions are obtained using the Monte Carlo method (MCM) based on the law of propagation of distributions (LPD). Here we also obtain the probability distributions and the coverage interval for the quantities measured with the calibrated instrument. Furthermore, motivated by the model structure of this particular example, we conducted a simulation study that presents the empirical coverage probabilities of the ISO and MCM coverage intervals and investigates the influence of the sample size, i.e. the number of calibration points in the measurement range, and the different combinations of measurement uncertainties. The study generally confirms the good properties and validity of the ISO technical specification within the considered (limited) framework of experimental designs motivated by real-world application, with small uncertainties in relation to the measurement range. We also point out the potential weaknesses of this method that require increased user attention and emphasise the need for further research in this area.

ISO Linear Calibration and Measurement Uncertainty of the Result Obtained With the Calibrated Instrument

Faculty of Mechanical Engineering of the Slovak University of Technology in Bratislava

Measurement Science Review

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

We address the problem of linear comparative calibration, a special case of linear calibration where both variables are measured with errors, and the analysis...

ISO Linear Calibration and Measurement Uncertainty of the Result Obtained With the Calibrated Instrument

Publié en ligne: 13 oct. 2022

Pages: 293 - 307

Reçu: 28 avr. 2022

Accepté: 21 sept. 2022

DOI: https://doi.org/10.2478/msr-2022-0037

Mots clés
Linear comparative calibration, ISO Technical Specification 28037:2010, Monte Carlo method, measurement uncertainty, calibrated instrument, empirical coverage probability

© 2022 Jakub Palenčár et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

ISO Linear Calibration and Measurement Uncertainty of the Result Obtained With the Calibrated Instrument

Publié en ligne: 13 oct. 2022

Pages: 293 - 307

Reçu: 28 avr. 2022

Accepté: 21 sept. 2022

DOI: https://doi.org/10.2478/msr-2022-0037

Mots clésLinear comparative calibration, ISO Technical Specification 28037:2010, Monte Carlo method, measurement uncertainty, calibrated instrument, empirical coverage probability

© 2022 Jakub Palenčár et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
Linear comparative calibration, ISO Technical Specification 28037:2010, Monte Carlo method, measurement uncertainty, calibrated instrument, empirical coverage probability