Expression of uncertainty in measurement

The New Perspective of the GUM

The Joint Committee of Guides in Metrology has decided that a revision of the Guide to the Expression of Uncertainty in Measurement (GUM, JCGM 100:2008) is necessary. Since the first publication of the GUM in 1993 (and its re-edition as JCGM 100:2008), the need to evaluate measurement uncertainty has been recognized in an increasing number of scientific disciplines, for which the JCGM 100:2008 does not provide sufficient guidance. This has probably inhibited the wide use of the GUM in some scientific disciplines, such as chemistry and biology, in which a definition of the measurand according to the requirements of the JCGM 100:2008 can be impossible. This perspective has been approved by the JCGM and also by ISO.

The Guide to the Expression of Uncertainty in Measurement has long been the authoritative document concerning the evaluation and expression of measurement uncertainty. The current structure (Guide vs. Supplements) of these documents no longer reflects the relationships that exist among and between them, nor offers a rational accommodation of future requirements. In 2014, the JCGM-WG1 started rethinking the structure of the suite of documents it maintains and develops. The aims of this rethinking were to restructure the JCGM 100-series of documents in such a fashion that it was easier to:

1. understand what document is relevant for a particular purpose,

2. develop documents with differing levels of complexity, and

3. establish a new focal point, namely the introduction to the suite of documents.

To underline the relationship between the documents and their commonalities, the entire suite of documents will be published under the common umbrella title “Guide to the Expression of Uncertainty in Measurement” and the established acronym GUM. An introductory document sets the scene for the expression, evaluation and use of measurement uncertainty; it gives a general outline of what is involved and directs the reader to the document of interest. In addition, all other GUM documents focus on a specific purpose, for example:

1. Application of the Gauss law of uncertainty propagation (JCGM 100:2008)

2. Propagation of distributions (JCGM 101:2008)

3. Measurements involving multiple measurands (JCGM 102:2011)

4. Measurement models (JCGM 103)

5. Least squares methods (JCGM 107)

6. Bayesian methods (JCGM 108)

7. Interlaboratory comparisons (JCGM 109)

This new structure emphasizes that users with different measurement problems require different guidance, which will now be available in stand-alone documents. For example, to apply the Monte Carlo method for a single measurand, the reader will only need JCGM 101:2008. The new structure enables the JCGM to respond in a flexible manner to emerging needs from the measurement community.

JCGM 103

Significant efforts at the JCGM-WG1 are spent in finalizing the document JCGM 103 which deals with developing and using measurement models. This document discusses the uncertainties that are inherent in the choice of models: theoretical, empirical, or hybrid. Uncertainties arise when analysts are faced with making choices between competing theoretical models (what approximations to make?), competing statistical models (fixed effects or random effects models), or competing empirical models (linear or quadratic approximation, what splines to adopt?). The JCGM 103 also discusses numerical issues that arise in nonlinear models and ways to deal with them (reparametrization, improved numerical methods, or change of mathematical framework in empirical models (monomial vs Chebyshev representation, for example)). The Committee draft will be circulated shortly.

Other Business

Two manuscripts of general interest have been published in Metrologia by members of the JCGM-WG1. The first document (Possolo and Pintar 2017 Metrologia 54 617; https://doi.org/10.1088/1681-7575/aa7e4a) discusses the plurality of choices that can reasonably be made when performing uncertainty evaluation. The manuscript shows that different choices typically lead to different estimates of the quantities of interest, and to different evaluations of the associated uncertainty. This manuscript lends support for the new paradigm of the GUM whereby the various choices within the uncertainty estimation are welcomed by the equal status of the various GUM documents.

The second document (Cox and Shirono 2017 Metrologia 54 642; https://doi.org/10.1088/1681-7575/aa787f) addresses the ‘small n problem’ which has been arguably the most critiqued aspect of the revised draft GUM of 2014. In short, non-informative Bayesian approach to uncertainty evaluation from a number n of replicate observations provides standard uncertainty of the mean (s/sqrt(n))*sqrt((n – 1)/(n – 3)) instead of the frequentist estimate of s/sqrt(n). The inapplicability of the former expression in situations when n < 4 has drawn lots of criticism from IUPAC and IFCC, among others. This article provides informative Bayesian estimate of uncertainty applicable for all n (n > 1) based on prior knowledge for the upper bound of the standard uncertainty.

For further information, contact Juris Meija <Juris.Meija@nrc-cnrc.gc.ca>, IUPAC representative on JCGM