Examples in major areas demonstrating choice of method

The aim of this work package is to develop worked examples of uncertainty evaluations in major areas in industry, trade, science and regulation. The examples illustrate the practical and theoretical deliberations underlying the choice of an appropriate method for uncertainty propagation, including (a) the law of propagation of uncertainty (JCGM 100, JCGM 102), (b) a Monte Carlo method (JCGM 101, JCGM 102), or (c) a Bayesian method (JCGM 108 – under development). Such examples are urgently needed to aid the user of the cited guidance documents to make an informed choice.  This work package is strongly related to the GUM New Perspective.

Factors that dictate choice of method will be brought out in many examples, including examples in which:

  • The law of propagation of uncertainty and a Monte Carlo method are compared for the quantification of low masses of benzo[a]pyrene.
  • Sample measurements of contaminants in soil are examined using several approaches to show how limited knowledge can be used most efficiently.
  • The adequacy of a straight-line function in calibrating sonic nozzles is considered against more general functions.
  • Analysis-of-variance (ANOVA) approaches are applied to reference material production and certification in the case of gas mixtures, illustrating the advantages of using Bayesian methods over classical statistics.
  • GUM and Bayesian-based approaches are contrasted in two examples related to very small volume and flow.



Comparison of average areal rainfall methods.  The growing awareness of the impact of climate change and the United Nations’ sustainable development goals show the need to have reliable measurement of quantities such as precipitation and rainfall to support management of water resources. Rainfall measurements obtained at several stations allow average areal rainfall using various methods to be calculated: arithmetic mean, Thiessen polygons (polygons whose boundaries define the area that is closest to each point relative to all other points) and isohyetal (isohyets are contours of equal precipitation). The uncertainties associated with the derived values play a strong role in the comparison of the accuracy of the methods.

Quantification of small masses of benzo[a]pyrene (BAP).  Two approaches for the evaluation of uncertainty associated with small masses of (BAP) provide different results for real data sets.  A Monte Carlo approach gives longer but more reliable coverage intervals than provided by the GUM, which presumes underlying normality.  Importantly, in cases of analyte masses close to zero, assumptions inherent in the GUM approach give coverage intervals that extend into regions of infeasible negative values whereas the Monte Carlo approach ensures feasibility

Greenhouse gases. The Intergovernmental Panel on Climate Change (IPCC) is the United Nations’ body for assessing the science related to climate change. In the context of greenhouse gas emissions, IPCC uncertainty guides consider the law of propagation of uncertainty (LPU) in the GUM and Monte Carlo (MC) for uncertainty propagation, stating that LPU is a useful quality control check on MC. That attitude is orthogonal to JCGM-WG1 principles, which use MC as a “gold standard” to validate other methods. Following completion of activity in the area, IPCC will be approached for discussion of this vital point.



Water resource management. Clean water and sanitation are among the sustainable development goals of the United Nations’ 2030 agenda  Growing demand increases the need to improve water management in society. Using data provided by a sequence of volume measurements, an example of how measurement uncertainty supports the analysis of performance and risk related to these utilities is provided.

Flow measurement according to ISO 5167-2.  For flow measurement, the uncertainty of the orifice-plate discharge coefficient given by the Reader-Harris/ Gallagher (1998) equation has been calculated taking account of the uncertainty of the data on which it is based and of the variability in manufacture permitted by ISO 5167-2.  Because the value produced is very similar to that in ISO 5167-2, the standard does not need to be changed and hence confidence in the use of this important standard is increased.  Some €20 Bn of natural gas each year in the UK alone is measured by devices conforming to ISO 5167.

Thermal comfort and energy saving.  Thermal comfort is quantified in ISO 7730, Ergonomics of the thermal environment, by an index depending on metabolic rate, air temperature, convective heat transfer, etc. For typical scenarios, the index was calculated and its uncertainty evaluated using GUM and Monte Carlo methods. The probability distribution obtained from Monte Carlo is far from normal whereas the GUM assumes normality. The practical repercussions of these observations are being communicated to committee ISO/TC 159/SC 5, Ergonomics of the physical environment.


Quality of life

Magnetic resonance based EPT.  Magnetic resonance-based electrical properties tomography (EPT) is used for cancer characterization. A Monte Carlo method is being applied at different values of specific parameters such as spatial correlation and the mesh resolution to understand their impact on the measurand.  Application is currently to a 2D model problem in which virtual measurements are given by numerical simulations and an additive Gaussian noise is superimposed on the total field (spatially uncorrelated noise and different signal-to-noise ratios).

Microflow.  Work has been carried out collaboratively with the health sector in Portugal, aimed at addressing quality issues related to the instrumentation used in hospitals, such as the need for calibration, traceability and quality of flow measurement.  Uncertainty evaluation, however, has not yet been treated in detail in hospitals in this area. 

Because values of some quantities were close to their physical limit, Bayesian methods are appropriate.  A paper on the topic was presented at the IMEKO TC7 conference in July 2019.

Rheology measurement.  This activity specifies general methods for the calibration of rheometers and evaluates the measurement uncertainty associated with the complex mathematical expression of viscosity derived for rotational rheometer equipment (a rheometer measures the way in which a liquid flows in response to applied forces). The Monte Carlo (MC) method of JCGM 101 has been used to validate the more commonly used GUM approach.  MC results yield a probability distribution for the measurand that is Gaussian in appearance but similarity to the Gaussian PDF provided by the GUM is deceptive: the GUM approach overstates the uncertainty by 50 %.


Industry and society

In-flight thrust.  Previous work covering ultrasonic thrust measurement technology has been reviewed. The measurand, in-flight thrust, is 

specified by a non-linear integral equation containing adjustable parameters. A forthcoming aircraft engine trial will provide data constituting measurements of gas temperature, velocity, etc. The solution of the integral equation that best matches the measured data will provide an in-flight thrust estimate and the associated uncertainty

Hardness. The status of uncertainty evaluation in ISO hardness standards, deploying two methods for determining uncertainty, has been evaluated. The results of the evaluation of the procedures for both methods have been compared.  First results have been presented at two conferences and will be shortly offered to ISO committee TC 164 as potential material for the improvement of hardness standards.

MOMS.  The evaluation of measurement uncertainty related to the calibration of a mobile optical measurement system (MOMS), based on the use of an SI-traceable reference standard, is considered. The measurement system studied contains three linear CCD cameras, in different spatial positions and orientations, with overlapping fields of view, permitting the simultaneous observation of an infrared LED located in a region of interest. By applying triangulation techniques, the measuring system can determine the static and dynamic spatial position of a set of observed LEDs.

Doping control.  A test programme to explore the influence of choice of uncertainty evaluation method on the quantification of threshold substances in doping control has commenced.  The first two of three proficiency testing trials has been completed and the third is under way.  A report from the trials, with accompanying data, will be elaborated for the relevant EMUE activity.