# 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.

Acknowledgements:

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

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/

For contacts:
Bibliography:

1. Kozin V. Z. Testing of mineral raw materials. Yekaterinburg, Publishing house of UGSU, 2011, 316 p. [In Russ].

2. Bashlykova T. V., Pakhomova G. A., Lagov B. S., Zhivaeva A. B., Doroshenko M. V., Karabasov Yu. S. Technological aspects of rational subsoil use. Moscow, MISIS, 2005, 576 p. [In Russ].

3. Morozov V. V., Khurelchuluun I., Dalgerbat L. Control of crushing and screening processes using visiometric ore analysis. Non-ferrous Metals. 2021, no. 7, pp. 17–23. [In Russ]. DOI: 10.17580/tsm.2021.07.01.

4. Morozov V. V., Topchaev V. P., Ulitenko K. Ya., Ganbaatar V., Dalgerbat L. Development and application of automated control systems for the processes of mineral enrichment, Moscow, Publ. house “Ore and metals”, 2013, 508 p. [In Russ].

5. Varlamova S. A., Zatonsky A. V., Fedoseeva K. A. Investigation of sensitivity to illumination of the method of glare recognition of potassium foam flotation machines. Ore dressing. 2021, no. 6, pp. 29–33. [In Russ]. DOI: 10.17580/or.2021.06.05.

6. Morozov V. V., Stolyarov V. F., Konovalov N. M. Improving the efficiency of flotation management using in-line pulp composition analyzers. Ore enrichment. 2003, no. 4, pp. 33–36. [In Russ].

7. Kejonen I., Haavisto O., Martikainen J., Suontaka V., Musuku B. Improving grade control efficiency with rapid on–line elemental analysis. Minerals Engineering. 2018, vol. 124, pp. 68–73.

8. Engströrn K., Esbensen K. H. Evaluation of sampling systems in iron concentrating and pelletizing processes — Quantification of Total Sampling Error (TSE) vs. process variation. Minerals Engineering. 2028, vol. 116, pp. 203–208.

9. Kudryavtsev V. Yu., Galass T. Yu., Stepanova I. S., Drobyshev A. A. Technical control as a tool to increase the competitiveness of the plant’s products. Mining Journal. 2022, no. 6, pp. 49–53. [In Russ]. DOI: 10.17580/gzh.2022.06.05.

10. Yakimov I. S., Bezrukova O. E., Dubinkin P. S., Shimansky A. F. X-ray technological control at the enterprises of the mining and metallurgical complex of non-ferrous metallurgy. Non-ferrous Metals. 2019, no. 9, pp. 56–62. [In Russ]. DOI: 10.17580/tsm.2019.09.09.

11. Ramsey M. H., Ellison S. L. R., Rostron P. et al. Measurement uncertainty arising from Sampling: a guide to methods and approaches — 2nd edition, Eurachem. 2019, 109 p.

12. Shemetov P. A. Quality management of ore flow at cyclic-flow technology of development of complex-structured deposits. Mining magazine. Special issue. 2002, pp. 80–83. [In Russ].

13. Sokolov A. D., Demsky M. I. Industrial installation of the GAA “Au-isomer”. Gold mining. 2021, no. 12 (277), pp. 23–25. [In Russ].

14. Verkhozin S. S. OLGA: Gekko Systems gold flow analyzer. Gold mining. 2021, no. 9 (274), pp. 14–19. [In Russ].

15. Napier-Munn T. J., Whiten W. J., Faramarzi F. Bias in manual Sampling of rock particles. Minerals Engineering. 2020, vol. 153, article 106260.

16. Lyapin A. G. Innovations of technical control. Mining magazine. 2019, no. 7, pp. 30–31. [In Russ].

17. Svensmark B. Extensions to the theory of sampling. 1. The extended Gy’s formula, the segregation paradox and the fundamental sampling uncertainty (FSU). An. Chim. Acta. 2021, vol. 1187, 339127. https://doi.org/10.1016/j.aca.2021.339127.

18. Karpenko N. V. Testing and quality control of ore dressing products, Moscow, Nedra, 1987, p. 216. [In Russ].

19. Leonov R. E., Sosnovskaya D. V. S. Model of ore clarification in a thickener. MIAB. Mining Inf. Anal. Bull. 2022, no. 11−1, pp. 190–198. [In Russ]. DOI: 10.25018/0236_1493_2022_111_0_190.

20. Ovchinnikova T. Yu., Tsypin E. F., Efremova T. A., Arinov K. N. Interrelation of surface and volume contents of components in pieces with different mineralization. MIAB. Mining Inf. Anal. Bull. 2022, no. 11−1, pp. 140–154. [In Russ]. DOI: 10.25018/0236_1493_2022_111_0_140.

21. Tsypin E. F., Efremova T. A., Ovchinnikova T. Yu. Modeling of the X-ray fluorescence separation process. MIAB. Mining Inf. Anal. Bull. 2022, no. 11−1, pp. 127–139. [In Russ]. DOI: 10/25018/0236_1493_2022_111_0_127.

22. Ovchinnikova T. Yu., Efremova T. A., Tsypin E. F. On the lower limits of the size classes during preliminary ore enrichment using X-ray fluorescence separation. MIAB. Mining Inf. Anal. Bull. 2021, no. 11−1, pp. 328–337. [In Russ]. DOI: 10/25018/0236_1493_2021_111_0_328.

23. Liu Q., Shi F., Wang X., Zhao M. Statistical estimation of blast fragmentation by applying 3D laser scanning to muck pile. Shock and Vibration. 2022, vol. 15, pp. 1–15. DOI: 10.1155/2022/3757561.

24. Carlsson G. Topological methods for data modelling. Nature Reviews Physics. 2020, no. 2, pp. 697–708.

## Our partners

### Подписка на рассылку

Раз в месяц Вы будете получать информацию о новом номере журнала, новых книгах издательства, а также о конференциях, форумах и других профессиональных мероприятиях.