Examples related to metrological activities adaptable as template solutions

The aim of this work package is to develop new and updated examples of measurement uncertainty evaluation capable of acting as template solutions that end-users can adapt for their own applications. The examples include measurement model construction using the JCGM modelling document JCGM 103 (being finalized), the application of the law of propagation of uncertainty and the Monte Carlo method [JCGM 100 (the GUM), JCGM 101 and JCGM 102], the application of principles for addressing conformity assessments, for example, according to JCGM 106, and taking correlation into account.

Currently, the state of the art in many calibration and testing laboratories is such that a measurement model relating the measurand and the (input) quantities that influence it is not explicitly taken into account. The starting point is instead only the sources of uncertainty, from which an uncertainty budget is developed. There are dangers in dispensing with the measurement model in that an adequate relationship between the measurand and the input quantities may not have been considered. Moreover, the sensitivity coefficients required in applying the law of propagation of uncertainty in the GUM may be difficult to obtain in some cases. All examples in the project relate to modelling, some in terms of the construction of the model, and some in terms of a comparison of a simple and a sophisticated model, fully in accordance with the principles in the GUM and other JCGM documents, and is assisting in finalizing the modelling document JCGM 103.

Equally, all examples are concerned with the propagation of uncertainties through a measurement model according to JCGM 100 (for single measurands) or JCGM 102 (for multivariate measurands). In some instances, a Monte Carlo method (JCGM 101, JCGM 102) is also applied, where probability distributions (normal, rectangular, etc.) for the input quantities are propagated through the model. For the Monte Carlo method, the way these probability distributions are selected, based on available metrological knowledge, is emphasized. In most examples a comparison is made of the relative merits of different methods for uncertainty propagation and conclusions drawn, so feeding into the New Perspective to the GUM. The GUM New Perspective is greatly broadening the scope of the original GUM. In some cases, a Bayesian approach will be used, for which a guidance document is being developed by JCGM-WG1. Inherent advantages when there are natural limits on the quantities involved (such as purity expressed as mass fraction, say, not exceeding 100 %), are emphasized.


Progress on activities in Work Package 1

Calibration, testing and comparison

Two-point and multi-point interpolation.  A generic approach for two-point and multi-point interpolation has been provided accounting for uncertainty and covariance associated with both variables. Possible deficiencies in the ways calibration laboratories handle such data are discussed. The approach has been applied to the measurement of hydrogen ion activity (pH).  In one instance of the analysis of pH measurement, a two-point bracketing technique was applied several times to deliver the required result.


Straight-line regression.  The reliability of conventional approaches for straight-line calibration has been compared with a generic treatment that takes account of stimulus and response uncertainties and covariances. Errors-in-variables regression models are employed.  Advice is given on circumstances where ordinary least-squares are applicable to such problems.  A paper on the topic has been submitted to a metrology journal.


 Mass calibration. Guide JCGM 101 concerned with a Monte Carlo method for uncertainty propagation includes an example of mass calibration.  A Bayesian method is applied to mass calibration and the results obtained compared with those from Monte Carlo and the law of propagation of uncertainty in the GUM (JCGM 100).  The effect of various prior distributions on the results is considered.



Single Burning Item reaction to fire test.  The application of the Monte Carlo method (MCM) in JCGM 101 for uncertainty propagation is applied to the Single Burning Item test, within the European normative framework of reaction to fire tests for building products, namely, EN standard 13823:2010+A1. The use of MCM is justified by the multivariate, non-linear and complex nature of the functional relations between a large number of input, intermediate and output quantities, thus providing a numerical approach to the validation of the GUM method.


Reassessment of calibration and measurement capabilities based on key comparison results.  A Bayesian method has been developed for the minimal adjustment of CMC (calibration and measurement capability) uncertainty claims so they are supported by the results of a key comparison (KC). CMC uncertainties are the expanded measurement uncertainties available to customers under normal conditions of measurement. When laboratories’ CMC claims are unsupported by the relevant KC, modified values are to be assigned to their declared CMC uncertainties.  The method has been applied to gauge block comparison and accelerometer comparison.

Linking of RMO and CIPM key comparisons.  The linking of regional metrology organization (RMO) and International Committee of Weights and Measures (CIPM) key comparisons (KCs) is considered in terms of statistical testing.  The derivation of a unilateral DoE based on an explicit statistical model without any biases and its characterization based on realistic data are considered.  The method has been applied to comparisons in the area of vibration.  The results show that the unilateral degree of equivalence (DoE) given by this method could be significantly different from those given by other approaches. The implication is that a consultative committee should choose an analysis method in accordance with its intention to implement an RMO KC.


Conformity to regulation or specification

Conformity assessment of a multicomponent material.  The application of guide

JCGM 106, relating to a single quantity for which a conformance statement is required, can provide incorrect risks of making false decisions when applied to a multicomponent material. An approach for multicomponent materials has been produced and exemplified with data for influenza medication (NyQuil tablets). The results have been incorporated in an IUPAC/CITAC Guide. The work has also been submitted for publication in a journal.


Total Suspended Particulate (TSP) matter concentration in ambient air.  The concentration of TSP matter in ambient air in three industrial zones is studied.  The assumption of underpinning normality of the data is inappropriate. The producer’s and inhabitants’ global risks, depending on an upper acceptance limit, is calculated according to JCGM 106, considering the role of measurement uncertainty in the conformity assessment.


Atomic Force Microscopy (AFM) for measurement of nanoparticles.  A major bottleneck in nanoparticle measurements is the lack of data comparability between techniques and between laboratories, a problem that can be overcome by making the measurements traceable to the SI together with realistic uncertainty evaluation.  A Bayesian approach is used to perform measurement uncertainty evaluation in a framework where no comprehensive physical model is available. The method is applied to the dimensional measurement of nanoparticles using atomic force microscopy and the calibration is performed using a multiple‑points calibration curve. Uncertainty evaluation for nanoparticle size measurements is crucial in various EU regulations, for example, EU No 528/2012 concerning making biocidal products available on the market and their use.