The dependence of the permissible error of analyses on the mass fraction of the component being determined

The error of the analysis of the mass fraction of the component in the enrichment products is determined by the inevitable random error of the sample selection and the error of the measurement method. The dependences of the analysis errors on the mass fraction have the same form regardless of which method determines the component or which equipment performs the measurement. The generality of dependencies is predetermined by one procedure common to any analyses — the selection of the sample for analysis, and their identical appearance determines the role of the sample selection error over the errors of any measurement options for the mass fraction on these samples. Currently, they are trying to perform analysis with the help of various equipment, a characteristic feature of which is the unknown weight of the suspension. This mass is not only unknown, but it varies widely depending on the equipment used. The random sampling error of the sample can be calculated using an analytical formula that includes the sample weight and mass fraction. This allows us to obtain dependences of the random error on the mass fraction for a fixed weight of the suspension. As a result, the general dependence of the relative random error on the mass fraction is obtained, which completely coincides with the experimentally determined dependencies. But due to different conditions for assigning permissible errors: repeatability or reproducibility, accepted confidence probabilities, differences in the size of the attachments and fluctuations in their composition, the quality of work of performers, etc., theoretical and experimental dependences differ from each other. The presence of a theoretical dependence allows one reliably established value of the relative random error for the selected mass fraction to find an experimental coefficient and, as a result, to build the entire dependence.

Keywords: relative random error, sample for analysis, mass fraction, sample ratio, fundamental error formula, homogeneous arrays, sample uniformity, sample weight.
For citation:

Kozin V. Z., Komlev A. S., Stupakova E. V. The dependence of the permissible error of analyses on the mass fraction of the component being determined. MIAB. Mining Inf. Anal. Bull. 2023;(12−1):56—69. [In Russ]. DOI: 10.25018/0236_1493_2023_121_0_56.


The study was carried out with the support of the Ministry of Science and Higher Education of the Russian Federation in accordance with the state task No. 0833−2023−0004 for the Ural State Mining University.

Issue number: 12
Year: 2023
Page number: 56-69
ISBN: 0236-1493
UDK: 622.7.092
DOI: 10.25018/0236_1493_2023_121_0_56
Article receipt date: 15.05.2023
Date of review receipt: 07.08.2023
Date of the editorial board′s decision on the article′s publishing: 10.11.2023
About authors:

Kozin V. Z., Dr. Sci. (Eng.), professor, Ural State Mining University, Head of the department of mineral processing, Dean of the faculty of mining and mechanics, 30 Kuibyshev Str., Yekaterinburg, 620144, Russia;
Komlev A. S., Senior researcher, Cand. Sci. (Eng.), Ural State Mining University, department of mineral processing, 30 Kuibyshev Str., Yekaterinburg, 620144, Russia;
Stupakova E. V., Head of technical control service, PJSC «Rusolovo», 6 Leninsky Ave., Moscow, 119049, Russia/


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