Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-28T22:14:55.403Z Has data issue: false hasContentIssue false
  • English
  • Français

Approaches to evaluating measurement uncertainty

Published online by Cambridge University Press:  14 November 2012

A.B. Forbes
A.B. Forbes*
Affiliation:
National Physical Laboratory, TW11 0LW, Teddington, UK
*
⋆ Correspondence: Alistair.Forbes@npl.co.uk
Get access

Abstract

The Guide to the expression of measurement uncertainty, (GUM, JCGM 100) and its Supplement 1: propagation of distributions by a Monte Carlo method, (GUMS1, JCGM 101) are two of the most widely used documents concerning measurement uncertainty evaluation in metrology. Both documents describe three phases (a) the construction of a measurement model, (b) the assignment of probability distributions to quantities, and (c) a computational phase that specifies the distribution for the quantity of interest, the measurand. The two approaches described in these two documents agree in the first two phases but employ different computational approaches, with the GUM using linearisations to simplify the calculations. Recent years have seen an increasing interest in using Bayesian approaches to evaluating measurement uncertainty. The Bayesian approach in general differs in the assignment of the probability distributions and its computational phase usually requires Markov chain Monte Carlo (MCMC) approaches. In this paper, we summarise the three approaches to evaluating measurement uncertainty and show how we can regard the GUM and GUMS1 as providing approximate solutions to the Bayesian approach. These approximations can be used to design effective MCMC algorithms.

Keywords

Measurement uncertaintyMonte CarloMarkov chain Monte Carlo
Type
Research Article
Information
International Journal of Metrology and Quality Engineering , Volume 3 , Issue 2 , 2012 , pp. 71 - 77
Copyright
© EDP Sciences 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

JCGM 200, International vocabulary of metrology – basic and general concepts and associated terms (VIM), 2008
JCGM 100, Guide to the expression of uncertainty in measurement (GUM), 2008
JCGM 101, Guide to the expression of uncertainty in measurement – Supplement 1 : Propagation of distribution using the Monte Carlo method (GUMS1), 2008
H.S. Migon, D. Gamerman, Statistical Inference : an Integrated Approach (Arnold, London, 1999)
A. Gelman, J.B. Carlin, H.S. Stern, D.B. Rubin, Bayesian Data Analysis, 2nd edn. (Chapman & Hall/CRC, Boca Raton, 2004)
D. Gamerman, Markov Chain Monte Carlo (Chapman & Hall/CRC, Boca Raton, 1999)
G. Grimmett, D. Stirzaker, Probability and Random Processes, 3rd edn. (Oxford University Press, Oxford, 2001)
Elster, C., Wöger, W., Cox, M.G.. Draft GUM Supplement 1 and Bayesian analysis, Metrologia 44, L31–L32 (2007) CrossRefGoogle Scholar
Elster, C., Toman, B., Bayesian uncertainty analysis under prior ignorance of the measurand versus analysis using Supplement 1 to the Guide : a comparison. Metrologia 46, 261–266 (2009) CrossRefGoogle Scholar
Forbes, A.B., Sousa, J.A., The GUM, Bayesian inference and forward and inverse uncertainty evaluation. Measurement 44, 1422–1435 (2011) CrossRefGoogle Scholar
A.B. Forbes, An MCMC algorithm based on GUM Supplement 1 for uncertainty evaluation. Measurement. (in press, DOI : 10.1016/j.measurement.2012.01.018)
A.B. Forbes, A two stage MCM/MCMC algorithm for uncertainty evaluation, in Advanced Mathematical and Computational Tools in Metrology and Testing IX, Göteborg, Sweeden, 2011, edited by F. Pavese et al. (World Scientific, 2012), pp. 159–170
M.G. Cox, P.M. Harris, Uncertainty Evaluation, Report No. MS 6 (Software Support for Metrology Best Practice Guide 6) (National Physical Laboratory, Teddington, 2011)
J.A. Sousa, A.S. Ribeiro, A.B. Forbes, P.M. Harris, F. Carvalho, L. Bacelar, The relevance of using a Monte Carlo method to evaluate uncertainty in mass calibration, IMEKO TC3, TC16 and TC22 International Conference Merida, Mexico, 2007
Possolo, A., Toman, B., Assessment of measurement uncertainty via observation equations. Metrologia 44, 464–475, 2007 CrossRefGoogle Scholar
A.B. Forbes, Nonlinear least squares and Bayesian inference, in Advanced Mathematical and Computational Tools for Metrology VIII, edited by F. Pavese et al. (World Scientific, Singapore, 2009), pp. 103–111