Project Details Influence of a mass balance constraint on uncertainty of test results of a substance or material and risks in its conformity assessment

Project No.:
Start Date:
01 July 2019
End Date:


Series: Risks of conformity assessment of a multicomponent material or object in relation to measurement uncertainty of its test results

When components of a substance or material are linked by a mass balance constraint (sum of their mass fractions, molar fractions or any other positive quantity ratios is 100 % or 1), test results of the components’ contents are named “compositional data”. These data are correlated because of the constraint: the correlations are called “spurious”. Such correlations may influence measurement uncertainty of the test results, and therefore risks in conformity assessment of the substance or material. That is important in testing geological and environmental objects, products of metallurgical and food industries, etc. A special case is the evaluation of purity of substances and development of corresponding (pure) certified reference materials, based on a mass balance.

There is an extensive literature stressing how traditional statistical techniques may produce inadequate results if applied on raw compositional data without suitable transformation. However, the relevant techniques of the compositional data analysis are still not implemented in metrology and analytical chemistry, as well as in conformity assessment.


In the IUPAC project 2016-007-1-500 a general Bayesian approach was elaborated for evaluation of risks of false decisions in conformity assessment of multicomponent materials or objects, taking also into account possible correlations between the measured property values of an item’s components. This ‘conventional’ approach applies integration of the relevant posterior multivariate probability density function on the tolerance/specification multi-domain for evaluation of the item conformance probability and corresponding risks of false decisions in the conformity assessment.

In the case of a mass balance constraint, the components’ contents of a substance or material form a multi-dimensional simplex, to which, in general, Euclidean geometry cannot be straightforwardly applied. A problem in compositional data analysis is also influence of spurious correlations between test results on singular covariance matrices. Spurious correlations should be considered as well at evaluation of measurement uncertainty of the test results, e.g. when considering uncertainty of a substance purity equal to the difference between 100 % and the sum of the test results of impurities mass fractions.

In this project, we will study how to deal with compositional data in conformity assessment. The proposed approach consists in resorting to a Monte Carlo method taking into account the mass balance constraint. The influence of the mass balance constraint on measurement uncertainty and risks in conformity assessment will be highlighted.


January 2020 update – The preparations to organize an international workshop on metrology and quality of chemical analytical results has started. The workshop supported by IUPAC and CITAC will be organized in conjunction with ISRANALYTICA Conference and Exhibition and take place 19-20 Jan 2021, in Tel Aviv, Israel. The workshop will provide an opportunity for the task group to share its work with representatives of the chemical analytical community. See Workshop details.

May 2020 update – A position paper has been published: Francesca R. Pennecchi, Aglaia Di Rocco, Ilya Kuselman, D. Brynn Hibbert and Michela Sega. Correlation of test results and influence of a mass balance constraint on risks in conformity assessment of a substance or material, Measurement, 163 (2020).

Nov 2020 update – As a case study, the measurement results (measured values and associated measurement uncertainty) obtained for testing a potassium iodate batch, being considered as a candidate reference material of potassium iodate purity, are analyzed and discussed for different models of the prior probability density function and the likelihood function. See Measurement (Available online 30 Oct 2020),

Page last updated 12 Nov 2020