The European Centre for
Mathematics and Statistics in Metrology

“Novel mathematical and statistical approaches to uncertainty evaluation“


Involved MATHMET members
PTB (Germany), LNE (France), NPL (UK), SP (Sweden)
Project partners
CMI (Czech Rep.), INRIM (Italy), JV (Norway), VSL (Netherlands), Force (Denmark), LGC (France), LGC (UK)
08/2012 - 07/2015
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Background and Need for the Project

Measurement uncertainty evaluation is fundamental to metrology. Without it, measurement results cannot be compared, either among themselves or with reference values given in specifications and standards.
Metrological traceability requires the propagation of reliable uncertainty values from primary standards provided by national metrology institutes (NMIs) to industrial end users. Unreliable evaluation of uncertainties has a vast negative economic impact.

New mathematical and statistical approaches are required to address uncertainty evaluation in many modern metrology applications, which are not explicitly covered by existing GUM guidelines. For example, uncertainty evaluation in many emerging or rapidly growing metrology applications, such as biochemical measurements and nanometrology, often poses challenging mathematical and statistical problems. There exists an unnecessarily high risk of incorrect decisions without reliable measurement uncertainty analysis. Many applications demand guidance for conformity assessment beyond current standards. The specific needs in problems demanding inverse methods and regression or computationally expensive systems require a co-ordinated effort to cope with these challenges, to ensure harmonisation and to develop a consistent application framework throughout Europe.


The project is developping novel approaches to measurement uncertainty evaluation and aims to enable their consistent application, illustrated by appropriate case studies. The dissemination of these methods will be ensured by providing input for future revisions of the Guide to the Expression of Uncertainty in Measurement (GUM), its supplements and other relevant documents and by providing algorithms and software. It focuses on three areas where new uncertainty analysis methods are needed: inverse and regression problems, computationally expensive model functions, conformity assessment and reliable decision-making.

In addition, the project focuses on applying these methods to challenging applications where a strong need for new uncertainty evaluation methods has been identified. These include new analytical technologies for biochemistry and biotechnology (ELISA, PCR), transport processes (fluid flow, thermophysical properties of materials), industry and regulation (scatterometry, fire safety engineering, conformance testing for healthcare products). Case studies addressing these important areas are carried out in such a way that their solutions generate a large immediate impact. They will also provide template solutions that will be easy to use for other applications. Outputs from work packages include software, best practice guides, scientific papers and reports, articles in trade journals, conference presentations, and reference data sets.

The project builds on the existing network of mathematical experts active in the EURAMET Focus Group Mathematical and Software Tools for Metrology project and will lay the foundation for a virtual European Centre for Mathematics and Statistics in Metrology that will disseminate state of the art methods to European industry and organisations and ensure that the momentum developed by the project is carried forward and that impact can be realised beyond the end of the project.

This project aims at a substantial extension of the mathematical infrastructure for metrology in Europe. Collaboration between European NMIs with mathematical and statistical expertise is essential to ensure wide take-up of the project outputs and to maintain Europe’s current leading role in mathematics for metrology. The results of this project will strengthen European capabilities for innovation by enabling traceability for modern metrology and measurement techniques. Product testing, safety regulations, medical diagnosis and drug testing will be significantly improved by the procedures for reliable uncertainty evaluation, decision-making and conformity assessment to be developed in this project. Training courses provided by the Creating Impact work package will allow European NMIs and DIs that are not part of the project consortium to develop their capacity in the application of mathematics and statistics to challenging uncertainty evaluation problems. The planned virtual European Centre for Mathematics and Statistics in Metrology will be based in the first instance on the members of the current JRP-Consortium.

Application Partners and Stakeholders

At the international level JCGM Working Group 1 (JCGM/WG1) on the Expression of Uncertainty in Measurement, which represents BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML, has identified the need for research in the areas of Monte Carlo methods, regression and inverse problems, conformity assessment and the application of expert and prior knowledge. Many national professional societies of engineers and accreditation bodies have recognised the need for further development of uncertainty evaluation methods. These bodies maintain specialised committees dealing with the topic of uncertainty evaluation that regularly seek advice from NMI experts. European and international associations dealing with best-practice guides to the use of computationally expensive models have started to address questions of uncertainty.

23 stakeholders have expressed their strong interest in this project. The list includes industry, universities, professional societies, regulatory bodies, international organisation and NMIs outside Europe. The stakeholders will form an Application Partner and Stakeholder Committee whose role of will be to ensure that the outputs of the product have clear relevance to NMI experimentalists and to industrial stakeholders and end users. Committee members will also have a key role in testing and establishing the usability of software produced by the technical work packages.


Related scientific publications

M. Bär, C. Elster, C. Matthews, L. R. Pendrill and L. WrightNovel mathematical and statistical approaches to uncertainty evaluation: introducing a new EMRP research16th International Congress of Metrology2013
C. Elster, K. Klauenberg, M. Bär, A. Allard, N. Fischer, G. Kok, A. van der Veen, P. Harris, I. Smith, L. Wright, S. Cowen, P. Wilson and S. EllisonNovel mathematical and statistical approaches to uncertainty evaluation in the context of regression and inverse problems16th International Congress of Metrology2013
L. R. Pendrill and N. PeterssonMetrology of human-based measurements17th International Congress of Metrology2015
G. Ebrard, A. Allan and N. FischerA user-friendly software for a simple and validated implementation of GUM Supplement 117th International Congress of Metrology2015
A. Allard and N. FischerRecommended tools for sensitivity analysis associated to the evaluation of measurement uncertaintyAdv. Math. Comput. Tools Metrol. Test. IX, World Scientific vol 84 2012
S. Demeyer and N. FischerModelling expert Knowledge to assign Consensus Values in Proficiency TestsAdvanced Mathematical and Computational Tools in Metrology and Testing IX, World Scientific, vol 842012
S. Demeyer, N. Fischer, F. Didieux and M. BinacchiStatistical methods for conformity assessment when dealing with computationally expensive systems : application to a fire engineering case studyAdvanced Mathematical and Computational Tools in Metrology and Testing X, World Scientific vol 86 2015
K. Klauenberg, M. Walzel, B. Ebert and C. ElsterInformative prior distributions for ELISA analysesBiostatistics2015
L. WrightParameter Estimation from Laser Flash Experiment DataChapter 8 of Computational optimisation and applications in engineering and industry, S. Koziel and X. S. Yang (eds.), Springer2011
C. Elster, K. Klauenberg, M. Walzel, G. Wübbeler, P. Harris, M. Cox, C. Matthews, I. Smith, L. Wright, A. Allard, N. Fischer, S. Cowen, S. Ellison, P. Wilson, F. Pennecchi, G. Kok, A. van der Veen, and L. PendrillA Guide to Bayesian Inference for Regression ProblemsDeliverable of EMRP project NEW04 “Novel mathematical and statistical approaches to uncertainty evaluation”2015
L. Wright, S. P. Robinson and V. F. HumphreyPrediction of acoustic radiation from axisymmetric surfaces with arbitrary boundary conditions using the boundary element method on a distributed computing systemJ. Acoust. Soc. Am. 125, 1374-13832009
G. Lindner, S. Schmelter, R. Model, A. Nowak, V. Ebert und M. BärA Computational Fluid Dynamics Study on the Gas Mixing Capabilities of a Multiple Inlet SystemJ. Fluids Eng, 138(3), 0313022015
T. R. Emardson, P.O.J. Jarlemark, P. FlobergUncertainty evaluation in multivariate analysis - a test case study.J. Math. Model. Algorithm. 4, 289-3052005
S. Heidenreich, H. Gross, M.-A. Henn, C. Elster, and M. Bär A surrogate model enables a Bayesian approach to the inverse problem of scatterometryJ. Phys. : Conf. Ser. 490, 0120072014
A. Allard, N. Fischer, F. Didieux, E. Guillaume and B. IoossEvaluation of the most influent input variables on quantities of interest in a fire simulationJ. Soc. Fr. Stat. 152,103-117.2011
H. Gross, S. Heidenreich, M. A. Henn, F. Scholze and M. BärModelling line edge roughness in periodic-line space structures by Fourier optics to improve scatterometryJEOS, vol. 9, 14003 (10pp)2014
L R Pendrill and W P Fisher JrQuantifiying Human Response: Linking metrological and psychometric characterisations of Man as a Measurement InstrumentJournal of Physics Conference Series 459 (2013) 0120572013
M.-A. Henn, H. Gross, S. Heidenreich, F. Scholze, C. Elster, and M. BärImproved reconstruction of critical dimensions in extreme ultraviolet scatterometry by modeling systematic errorsMeas. Sci. Tech. 25, 0440022014
O. Bodnar, A. Link, K. Klauenberg, K. Jousten, and C. ElsterApplication of Bayesian model averaging using a fixed effects model with linear drift for the analysis of key comparison CCM.P-K12Meas. Tech. 56, 584-5902013
A. Allard, N. Fischer, G. Ebrard, B. Hay, P. M. Harris, L. Wright, D. Rochais, J. MattoutA multi-thermogram based Bayesian model for the determination of the thermal diffusivity of a materialMetrologia2016
Giovanni Mana and Carlo PalmisanoInterval estimations in metrologyMetrologia 51, 91-96 2014
GJP Kok, AMH van der Veen, PM Harris, IM Smith, C ElsterBayesian analysis of a flow meter calibration problemMetrologia 52, 392-3992015
K. Klauenberg, G. Wübbeler, B. Mickan, P. M. Harris, and C. ElsterA Tutorial on Bayesian Normal Linear RegressionMetrologia, 52(6)2015
K. Klauenberg and C. ElsterMarkov chain Monte Carlo methods: an introductory exampleMetrologia, 53(1), S322016
L. R. PendrillUsing measurement uncertainty in decision-making & conformity assessmentMetrologia, Vol 51, S206 - S2182014
Andrea Malengo and Francesca PennecchiA weighted total least-square algorithm for any fitting model with correlated variablesMetrologia, vol. 50, nr. 6, 654-6222013
L. R. Pendrill, R. Emardson, B. Berglund, M. Gröning, A. Höglund, A. Cancedda, G. Quinti, F. Crenna, G. B. Rossi, J. Drnovsek, G. Gersak, T. Goodman, S. Harris, G. van der Heijden and K. KallinenMeasurement with persons: a European networkNCSLi Measure 5, 42-542010
S. Heidenreich, H. Gross and M. BärAlternative methods for uncertainty evaluations in EUV scatterometryProc. SPIE: Modeling aspects in Optical metrology IV2013
L. R. PendrillRisk assessment and decision-makingTheory and methods of measurements with persons, B. Berglund, G. B. Rossi, J. Townsend and L. R. Pendrill (eds.), Psychology Press, Taylor & Francis.2011
G. W. A. M. van der Heijden and R. EmardsonMultivariate measurementsTheory and methods of measurements with persons, B. Berglund, G. B. Rossi, J. Townsend and L. R. Pendrill (eds.), Psychology Press, Taylor & Francis.2011
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This work is part of the European Metrology Research Programme (EMRP) project NEW04. The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union.
More information can be found here.
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