The method for processing of the measurement results obtained from Comite International des Poids et Measures (CIPM) Key, Regional Metrology Organizations (RMO) or supplementary comparisons, from the proficiency testing by interlaboratory comparisons and the calibrations is proposed. It is named by authors as adjustment by least square method (LSM). Additive and multiplicative parameters for each measuring standard of every particular laboratory will be the results of this adjustment. As well as the parameters for each artifact.
The parameters of the measurements standards are their additive and multiplicative degrees of equivalence from the comparison and the estimations of the systematic errors (biases) from calibrations. The parameters of the artifacts are the key comparisons reference value from the comparison and the assigned quantity values from the calibrations.
The adjustment is considered as a way to solving a problem of processing the great amount of homogeneous measurements with many measuring standards at a different comparison levels (CIPM, RMO or supplementary), including connected problems.
Four different cases of the adjustments are considered. The first one is a free case of adjustment. It was named so because of the fact that none of participants has any advantage except their uncertainties of measurements.
The second one is a fixed case of adjustment. Measuring results of RMO and supplementary comparisons are rigidly linked to additive and multiplicative parameters of measuring standards of particular laboratories participated in CIPM key comparisons.
The third one is a case of adjustment with dependent equations. This one is not so rigidly linked of the new comparisons results to previous or to some other comparisons as for fixed case. It means that the new results of comparisons are influenced by the known additive and multiplicative parameters and vice versa.
The fourth one is a free case of adjustment with additional summary equations. In that case certain checking equations are added to the system of equations. So, the sum of parameters multiplied by their weights of all measurement standards for particular laboratories participated in comparisons should be equal to zero.
MRA: Mutual recognition of national measurement standards and calibration and measurement certificate issued by national metrology institutes. International Committee for Weights and Measures. 14 October 1999, p. 45. https://www.bipm.org/en/cipm-mra/cipm-mra-documents
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
JCGM 100:2008, Evaluation of Measurement Data — Guide to the Expression of Uncertainty in Measurement. Joint Committee for Guides in Metrology (JCGM).
JCGM 200:2012, International Vocabulary of Metrology — Basic and General Concepts and Associated Terms (VIM). Joint Committee for Guides in Metrology (JCGM).
JCGM 102:2011 Evaluation of measurement data — Supplement 2 to the «Guide to the expression of uncertainty in measurement» Extension to any number of output quantities. Joint Committee for Guides in Metrology (JCGM).
Nielsen L. 2003 Identification and handling of discrepant measurements in key comparisons. Measurement Techniques. 46(5), pp. 513–522. https://doi.org/10.1023/A:1025373701977
Sutton C. M. 2004 Analysis and linking of international measurement comparisons. Metrologia. 41, pp. 272-277. http://iopscience.iop.org/0026-1394/41/4/008
Elster C., Chunovkina A. G., Woger W. 2010 Linking of a RMO key comparison to a related CIPM key comparison using the parameters of the linking laboratories. Metrologia. 47. https://iopscience.iop.org/article/10.1088/0026-1394/47/1/011
Koo A., Clare J. F. 2012 On the equivalence of generalized least-squares approaches to the evaluation of measurement comparisons. Metrologia. 49, pp. 340-348. http://iopscience.iop.org/article/10.1088/0026-1394/49/3/340
White D. R. 2004 On the analysis of measurement comparisons. Metrologia. 41, pp. 122-131. http://iopscience.iop.org/0026-1394/41/3/003
Velychko O. M. 2009 Estimation of data of international comparisons of national standards: basic requirements and procedures. [Оброблення даних міжнародних звірень національних еталонів: основні вимоги і процедури] Ukrainian Metrological Journal. 3, pp. 57-63 [In Ukrainian].
COOMET R/GM/14:2006 2008 Guide on Estimation of the COOMET Key Comparison Data [Руководство по оцениванию результатов ключевых сличений КООМЕТ]. (St. Petersburg: COOMET) p. 13. [In Russian].
Elster C., Toman B. 2013 Analysis of key comparison data: critical assessment of elements of current practice with suggested improvement. Metrologia. 50, p. 549. https://iopscience.iop.org/article/10.1088/0026-1394/50/5/549
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].
Lawson C., Henson R. 1986 Solving Least Squares Problems. Science. Head Editor phys.-mat. lit., p. 232.
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