Access the full text.
Sign up today, get DeepDyve free for 14 days.
C. Cecelski, B. Toman, Fong-Ha Liu, J. Meija, A. Possolo (2022)
Errors-in-variables calibration with dark uncertaintyMetrologia, 59
A. Balsamo, G. Mana, F. Pennecchi (2006)
The expression of uncertainty in non-linear parameter estimationMetrologia, 43
(2006)
Statistics -Vocabulary and symbols -Part 1: General statistical terms and terms used in probability
(2018)
Generalized polynomial comparative calibration: Parameter estimation and applications
V. Witkovský (2016)
Numerical inversion of a characteristic function: An alternative tool to form the probability distribution of output quantity in linear measurement models, 5
E. Iso (1993)
Guide to the Expression of Uncertainty in Measurement
T. Bartel, S. Stoudt, A. Possolo (2016)
Force calibration using errors-in-variables regression and Monte Carlo uncertainty evaluationMetrologia, 53
A. Possolo, H. Iyer (2017)
Invited Article: Concepts and tools for the evaluation of measurement uncertainty.The Review of scientific instruments, 88 1
R. Carroll (2006)
Measurement error in nonlinear models: a modern perspective
(2013)
Evaluation of the uncertainty of measurement in calibration
K. Klauenberg, Steffen Martens, A. Bošnjaković, M. Cox, A. Veen, C. Elster (2021)
The GUM perspective on straight-line errors-in-variables regressionMeasurement
M Milton, P. Harris, I Smith, A Brown, B. Goody (2006)
Implementation of a generalized least-squares method for determining calibration curves from data with general uncertainty structuresMetrologia, 43
F. Guenther, A. Possolo (2011)
Calibration and uncertainty assessment for certified reference gas mixturesAnalytical and Bioanalytical Chemistry, 399
C. Osborne (1991)
Statistical Calibration: A ReviewInternational Statistical Review, 59
V. Witkovský, G. Wimmer (2021)
Exact Confidence Intervals for Parameters in Linear Models With Parameter Constraints2021 13th International Conference on Measurement
S. Stoudt, A. Pintar, A. Possolo (2020)
Uncertainty evaluations from small datasetsMetrologia, 58
D. Cox, E. Snell (1968)
A General Definition of ResidualsJournal of the royal statistical society series b-methodological, 30
(2002)
Statistical Inference, Second Edition. Duxbury, ISBN 0-534-24312-6
(2010)
Determination and use of straight-line calibration functions
S. Kotz, S. Nadarajah (2004)
Multivariate T-Distributions and Their Applications
L. Kubácek (1995)
On a linearization of regression modelsApplications of Mathematics, 40
A. Kukush (2011)
Measurement Error Models
(2012)
International vocabulary of metrology -Basic and general concepts and associated terms (VIM)
S. Murphy, A. Vaart (1996)
Likelihood Inference in the Errors-in-Variables ModelJournal of Multivariate Analysis, 59
(2022)
CharFunTool: The characteristic functions toolbox (MATLAB)
V. Witkovský, G. Wimmer (2022)
Polycal - MATLAB algorithm for comparative polynomial calibration and its applicationsSeries on Advances in Mathematics for Applied Sciences
M Krystek, M Antón (2008)
A weighted total least-squares algorithm for fitting a straight lineMeasurement Science and Technology, 19
A. Malengo, F. Pennecchi (2013)
A weighted total least-squares algorithm for any fitting model with correlated variablesMetrologia, 50
I. Lira, C. Elster, W. Wöger (2007)
Probabilistic and least-squares inference of the parameters of a straight-line modelMetrologia, 44
I. Markovsky, S. Huffel (2007)
Overview of total least-squares methodsSignal Process., 87
M. Cox, A. Forbes, P. Harris, I. Smith (2004)
The classification and solution of regression problems for calibration
A. Kukush, S. Huffel (2004)
Consistency of elementwise-weighted total least squares estimator in a multivariate errors-in-variables model AX=BMetrika, 59
L. Kubácek (1988)
Foundations of Estimation Theory
(2010)
Software to support ISO/TS 28037
AbstractWe 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.
Measurement Science Review – de Gruyter
Published: Dec 1, 2022
Keywords: Linear comparative calibration; ISO Technical Specification 28037:2010; Monte Carlo method; measurement uncertainty; calibrated instrument; empirical coverage probability
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.