Reference materials: selection of algorithm for estimating the certified value and its uncertainty based on the results of an interlaboratory experiment

The use of reference materials is the most accessible tool for ensuring metrological traceability of measurement results in various industries, and the main criterion for selecting a reference material is its metrological characteristics, including the uncertainty of the certified value and verified metrological traceability. One of the sources of uncertainty of a reference material is the characterization method selected by the producer. The article describes a method for characterizing a reference material based on the results of an interlaboratory experiment using algorithms from GOST 8.532-2002 “State system for ensuring the uniformity of measurements. Certified reference materials of composition of substances and materials. Interlaboratory metrological certification”, ISO 33405:2024 “Reference materials – Approaches for characterization and assessment of homogeneity and stability” and other documents. The validity of the uncertainty of the certified value of a reference material based on the results of an interlaboratory experiment is analyzed. It is shown that in some cases the above uncertainty of the certified value is significantly lower than the uncertainty of the measurement methods used in the given interlaboratory experiment, and in some cases, it is lower than the uncertainty of the calibrators used, including reference materials. In this case, developers and producers of reference materials have the illusion of high accuracy of reference material characterization by the interlaboratory experiment comparable to methods based on the use of standards. The article describes cases of unreasonable uncertainty underestimation of the certified value of a reference material, for example, due to the so-called “dark uncertainties” of the participants in the interlaboratory experiment, due to the low efficiency of the method of mathematical processing of the interlaboratory experiment results associated with the unreasonable exclusion from the estimation of the certified value of the reference material of the results obtained in certain laboratories, as well as due to the inadequacy of the statistical model underlying the algorithms for processing the results of the interlaboratory experiment to actual experimental data. Various algorithms for estimating the certified value and standard uncertainty from the characterization of a reference material based on the results of an interlaboratory experiment are analyzed. It is shown that the approach proposed by Maurice Cox is effective for estimating the uncertainty from characterization in terms of high resistance to outliers. Based on this approach, the authors of the article have developed their own algorithms that can be used to estimate the commutability of reference materials and for other purposes. In order to increase confidence in the results of determining the metrological characteristics of reference materials in the Russian Federation and to ensure harmonization with international documents, it is recommended to use the Maurice Cox algorithm when revising GOST 8.532-2002.

1. Matschat R., Richter S., Vogl J. et al. On the way to SI traceable primary transfer standards for amount of substance measurements in inorganic chemical analysis. Analytical and Bioanalytical Chemistry, 415, 3057–3071 (2023). https://doi.org/10.1007/s00216-023-04660-4 ; https://elibrary.ru/wwxkpu

2. Barwick V. J. (eds.). Eurachem Guide: Terminology in Analytical Measurement – Introduction to VIM 3. 2nd ed. (2023).

3. CCQM Guidance note: Estimation of a consensus KCRV and associated Degrees of Equivalence. BIPM (2013), available at: https://www.bipm.org/documents/20126/28430045/working-document-ID-5794/49d366bc-295f-18ca-c4d3-d68aa54077b5 (аccessed: 12.05.2025).

4. Mandel J., Paule R. C. lnterlaboratory evaluation of a material with unequal numbers of replicates. Analytical Chemistry, 42(11), 1194–1197 (1970). https://doi.org/10.1021/ac60293a019

5. Mandel J., Paule R. C. Interlaboratory evaluation of a material with unequal numbers of replicates (correction). Analytical Chemistry, 43(10), 1287 (1971). https://doi.org/10.1021/ac60304a001

6. DerSimonian R., Laird N. Meta-analysis in clinical trials. Controlled Clinical Trials, 7(3), 177–188 (1986). https://doi.org/10.1016/0197-2456(86)90046-2

7. DerSimonian R., Laird N. Meta-analysis in clinical trials revisited. Contemporary Clinical Trials, 45(A), 139–145 (2015). https://doi.org/10.1016/j.cct.2015.09.002

8. Huber P. J. Robust estimation of a location parameter. The Annals of Mathematical Statistics, 35(1), 73–101 (1964). https://doi.org/10.1214/aoms/1177703732

9. Beaton A. E., Tukey J. W. The fitting of power series, meaning polynomials, illustrated on band-spectroscopic data. Technometrics, 16(2), 147–185 (1974). http://dx.doi.org/10.1080/00401706.1974.10489171

10. Mosteller F., Tukey J. Data Analysis and Regression. In 2 volums, vol. 1. Finance and Statistics, Moscow (1982). (In Russ.)

11. Cox M. G. The evaluation of key comparison data. Metrologia, 39, 589–595 (2002). https://doi.org/10.1088/0026-1394/39/6/10

12. Cox M. G. The evaluation of key comparison data: Determining the largest consistent subset. Metrologia, 44(3), 187– 200 (2007). https://doi.org/10.1088/0026-1394/44/3/005

13. Aronov P. M. Estimation of consensus value of interlaboratory measurement results accompanied by a minimum increase in associated uncertainty. Measurement Standards. Reference Materials, 15(4), 49–52 (2019). (In Russ.). https://doi.org/10.20915/2077-1177-2019-15-4-49-52 ; https://elibrary.ru/glzghv

14. Aronov P. M., Sobina E. P., Migal P.V. et al. New algorithms for estimating the value of the certified characteristic of reference materials of substances and materials by the method of interlaboratory certification. Measurement Standards. Reference Materials, 19(3), 93–102 (2023). (In Russ.). https://doi.org/10.20915/2077-1177-2023-19-3-93-102 ; https://elibrary.ru/dqjizj

15. Cochran W. G. The combination of estimates from different experiments. Biometrics, 10, 101–129 (1954). https://doi.org/10.2307/3001666