Measurements and Calculations as the Subject Matter of Modern Metrology

• Published in: Measurement techniques Vol. 65; no. 5; pp. 321 - 329
• Main Author: Levin, S. F.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2022; Springer; Springer Nature B.V
• Subjects: Analysis; Analytical Chemistry; Characterization and Evaluation of Materials; Functionals; General Problems of Metrology and Measurement Technique; Mathematical analysis; Mathematical models; Measurement; Measurement Science and Instrumentation; Measuring instruments; Metrology; Operators (mathematics); Physical Chemistry; Physics; Physics and Astronomy; Professional development; Software; Statistical analysis; Statistical methods; measurement problem; composition; error of inadequacy; probability distribution; convolution; measurement; measurement method; problem-solving method
• ISSN: 0543-1972; 1573-8906
• DOI: 10.1007/s11018-022-02089-2

The synonymy issue of measurements and calculations is considered, which long prevented the proper regulatory and procedural analysis of inadequacy issues for the mathematical models of measurement objects, i.e., one of the most important metrological problems. Conceptually, the solution to the problem of inadequacy in the identification of mathematical models using joint measurement data involves a transition from the synonymy of measurements and calculations to the principle of uniform measurement and calculation results. The paper gives a brief description of issues covered by the All-Union discussion on the applicability of probabilistic statistical methods in 1970–1990, which was prompted by Andrey Kolmogorov’s question about the objective meaning of probability. It is noted that in the course of the discussion, criticism was directed at the mathematical results that subsequently formed the basis of the Guide to the Expression of Uncertainty in Measurement and its supplements. The main results of mathematics as a universal scientific language related to the solution of measurement problems are analyzed, thus expanding the understanding of the subject matter of metrology. It is shown that from this point of view, modern metrology is a fundamental science about methods and means of representing the properties of measurement objects by means of mathematical models. While the elementary models consist of quantities and value distributions, more complex models are random functions, functionals, and operators. In addition to measuring instruments, representation means include computational tools having algorithmic, mathematical, and other software to solve measurement problems. It is noted that difficulties arising in the training and professional development of metrologists are related to the problem of inadequacy.