According to the authors point of view, absence of the accepted by metrological society software based on simple and understandable and at the same time flexible and multipurpose mathematical apparatus is one of the restrictions on the way to arrangement of international comprehensive comparisons with expanded group of participants (hereinafter — comprehensive comparisons). General methodology of measurements adjustment by the least square method (LSM) may be used for this mathematical apparatus.
Software named «Metrology Network» is defined. It was used for repeated processing of measurement results during the key comparisons of EURAMET.L-K1.2011 «Measurement of gage blocks by interferometer». «Metrology Network» software allowed to estimate simply and quickly systematic measurement error components of the gage blocks length measurement by each laboratory. They are called multiplicative and additive measurement standards degrees of equivalence. «Metrology Network» allowed to estimate strictly by LSM the uncertainties of length measurement. Additive degrees of equivalence are considered substantial and constant characteristics of the measurement standards for many laboratories. Thus, they coincide for steel and ceramic gage blocks. These additive degrees of equivalence may be used as corrections in the process of calibration or as the reference values for further comparisons.
The simulation of measurement results for international comprehensive comparisons with complicated structure was provided. For 120 laboratories divided into 12 groups, totally 2442 length measurements of the steel or ceramic gage blocks were provided. They form together 24 sets of 8 gage blocks and provide 24 loops of comparisons. Necessity to provide the adjustment by the least square method is caused by the fact that two subgroups from each group of three laboratories took part in two different related loops of comparison. As a conclusion, «Metrology Network» software easily managed this complicated task of adjustment. It allowed us to calculate each of 120 measurement standards additive degree of equivalence relative to the averaged zero for all measurement standards and multiplicative degree of equivalence relative to the averaged measurement unit.
Cox M. G. 2002 The evaluation of key comparison data. Metrologia. 39. pp. 589-595. https://iopscience.iop.org/article/10.1088/0026-1394/39/6/10
Kuzmenko Yu., Samoylenko O. 2018 Processing by least square method of the measurement results for key, regional and supplementary comparison of the measurement standards [Опрацювання методом найменших квадратів результатів вимірювань за ключових, регіональних та додаткових звірень еталонів]. Metrology and Devices. 70, pp. 3-13. [In Ukrainian]
Kuzmenko Iu., Samoilenko O. 2021 The measurements results adjustment by the Least Square Method. Measurements infrastructure. 1. https://mi-journal-online.org/index.php/journal/article/view/1/1
Matus M. and etc. 2015 Final report on EURAMET Key Comparison EURAMET.L-K1.2011: Measurement of gauge blocks by interferometry. EURAMET project # 1218. EURAMET. Vienna, Austria, p. 63.
Nazarov N. G. 2002 Metrology. Basic concepts and mathematical models. High School. p.348.
Lawson C., Henson R. 1986 Solving Least Squares Problems. Science. Head Editor phys.-mat. lit., p. 232.
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