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Measurement Uncertainty

SIG events

  • MU-SIG co-organised the ENBIS Spring meeting on Measurement Systems and Process Improvement, at NPL, 19-20 April 2010, at the National Physical Laboratory, London, Connie Borror, Arizona State University, Maurice Cox, National Physical Laboratory
  • ENBIS President Dr Andrea Ahlemeyer-Stubbe gave a presentation at the IMEKO World Congress, 7-11 September, 2009
  • MU-SIG session was held at ENBIS 9, Gothenburg, 21-23 September 2009
  • Joint Workshop of itENBIS and INRIM on “Mathematical and Statistical Methods for Metrology” (, at the INRIM, Torino (Italy), 30-31 May 2019
  • Virtual Joint Workshop of ENBIS and Mathmet on“Mathematical and Statistical Methods for Metrology” (, online, 31 May – 1 June 2021
  • Joint Workshop of ENBIS and Mathmet on “Mathematical and Statistical Methods for Metrology” (, to be held at the INRIM, Torino (Italy)30 – 31 May 2023.

MU-SIG Themes

The SIG has two complementary themes, 1) the application of statistical methods in measurement science (metrology), and 2) measurement systems in process control, conformance assessment and quality improvement.

Metrology – the science of measurement

The central aim of metrology is to establish the traceability of measurement results to standard units, providing a foundation for commerce, science and technology alike. National Metrology Institutes (NMIs) are responsible for defining and maintaining measurement standards at a national level, overseen by the Bureau International des Poids et Mesures (BIPM) at the international level. Historically, primary measurement standards have been realised as artefacts (a metre bar, a kilogram mass, etc.), but now are generally related to quantum phenomena, e.g., the second is defined as the duration of 9 192 631 770 periods of the radiation corresponding to a ground state transition of the caesium-133 atom.

Uncertainty evaluation in metrology

A central activity in metrology is the evaluation of uncertainty, a quantitative measure of the quality of measurement results, enabling them to be compared with other results, references, specifications or standards. Uncertainty evaluation is one of the main topics of interest for the European Metrology Network for Mathematics and Statistics (EMN Mathmet), of which ENBIS is one of the principal Stakeholders. It is mentioned as a backbone theme for all the scientific fields and metrological applications mentioned in the Mathmet Strategic Research Agenda (SRA), such as AI and machine learning algorithms as well as computational modelling and virtual metrology methods. Moreover, the MU-SIG is a Stakeholder of the Mathmet MU Training Activity that was launched in October 2021 with the aim to improve quality, efficiency and dissemination of measurement uncertainty training.

Documentary standards for the evaluation of uncertainty

Within the metrology community, uncertainties are evaluated according to the Guide to the Expression of Uncertainty in Measurement (“GUM”), and related documents, published and maintained by Working Group 1 of the BIPM’s Joint Committee for Guides in Metrology (JCGM). The document ISO 5725 Accuracy (trueness and precision) of measurement methods and results is used widely in industry. The Technical Specification ISO/TS 21748:2004  Guidance for the use of repeatability, reproducibility and trueness estimates in measurement uncertainty estimation shows how an ISO 5725 uncertainty analysis can be used in a GUM-type uncertainty evaluation.

The three-year EMPIR Project “EMUE – Examples of Measurement Uncertainty Evaluation” ( produced a comprehensive set of worked examples illustrating how principles of measurement uncertainty evaluation can support documentary standards and guides. All the results are open access and available at Zenodo repository.

Computational methods

The GUM uncertainty framework essentially uses the law of propagation of uncertainty to propagate expectations and standard deviations associated with input (influence) quantities through to an output quantity (measurand). GUM Supplement 1 on Propagation of distributions using a Monte Carlo method describes the use of Monte Carlo techniques. In recent years, Bayesian approaches to uncertainty evaluation have been implemented, some using Markov chain Monte Carlo simulation.

Interlaboratory comparisons

Interlaboratory comparisons (ILCs) are a key tool in determining the measurement performance of laboratories. In particular, the Mutual Recognition Arrangement (MRA) aims to

  • establish the degree of equivalence of national measurement standards maintained by NMIs, and
  • provide for the mutual recognition of calibration and measurement certificates issued by NMIs

using ILCs, with results maintained in a database hosted by BIPM. There are many statistical issues associated with the design of ILCs and the analysis and reporting of results.

Measurement systems in process control

Statistical quality control systems rely on measurement systems to provide data on key process or product characteristics. Often, problems initially associated with processes are found to be due to poorly performing measurement systems. Accuracy statements or specifications of performance do not always reflect the true influence of the measurement system on the observed process data. Standards such as ISO 10012:2003  Measurement management systems – Requirements for measurement processes and measuring equipment specify generic requirements and provide guidance for the management of measurement processes and metrological confirmation of measuring equipment used to support and demonstrate compliance with metrological requirements.

Measurement systems analysis (MSA) refers to assessing the capabilities of measurement systems relative to the metrological requirements. It includes techniques such as gauge repeatability and reproducibility tests. Coordinate measuring machines (CMMs) are replacing gauges as a tool for process control but there are many issues about how to assess their performance for a particular application and how to design measurement strategies that adequately capture the functionally relevant features of the parts being measured.

Conformance to specification

Inspection regimes are used to decide whether a part meets its design specification on the basis of measurement. Uncertainties associated with the measurement results mean that there are risks that a good part is rejected or a bad part passed. There are many design-of-experiment issues associated with minimising combined measurement and decision costs. Similar issues apply to environmental monitoring, e.g., assessing whether the emissions from a chimney stack conform to environmental legislation.

Links to other organisations


BIPM Bureau International des Poids et Mesures
CMM Coordinate Measuring Machine
GUM Guide to the Expression of Uncertainty in Measurement
ILC Interlaboratory Comparison
IMEKO International Measurement Confederation
ISO International Organization for Standardization
JCGM Joint Committee for Guides in Metrology
Mathmet European Metrology Network for Mathematics and Statistics
MRA Mutual Recognition Arrangement
MSA Measurement Systems Analysis
NMI National Metrology Institute

SIG chairman

The current chairman is Alistair Forbes,

  • Fellow in the Mathematics and Scientific Computing research group at the National Physical Laboratory
  • Visiting Professor of Industrial Mathematics at the School of Computing and Engineering, University of Huddersfield
  • Scientific Secretary, IMEKO TC21: Mathematical Tools for Measurement
  • Member of ISO TC 69: Application of Statistical Methods

Co-chair is Francesca Pennecchi,


The following topics were listed, that could be important to discuss in future (non-prioritised order):

– Verification of uncertainty budgets
– QA/QC use of uncertainty budgets
– Measurement uncertainty in health services
– CMM: Coordinate Measuring Machines
– Measurement uncertainty and conformity to specifications
– Measurement uncertainty and sampling inspection
– The role of measurement uncertainty in six sigma

At present the group considers itself an interest group more than a working group, i.e. it is our hope that the group can play as a network within the ENBIS network!

It is expected, that measurement uncertainty will play in increasing role at future ENBIS conferences. Meanwhile, we hope to be able to benefit from mutually contacting each other with exchanging relevant references, suggesting presentations for next ENBIS conferences, collaborating with Mathmet on topics of common interest, etc.