Journals →  Obogashchenie Rud →  2022 →  #3 →  Back

ArticleName Calculation of relative random errors in the sampling of processing products
DOI 10.17580/or.2022.03.05
ArticleAuthor Kozin V. Z., Komlev A. S., Stupakova E. V.

Ural State Mining University (Ekaterinburg, Russia).

Kozin V. Z., Head of Chair, Doctor of Engineering Sciences, Professor,
Komlev A. S., Senior Researcher, Candidate of Engineering Sciences,


Irgiredmet (Irkutsk, Russia):
Stupakova E. V., Head of Department


This paper discuses random errors occurring in processing product sampling, preparation, and assays. Separate identification of variouserror components prevents comprehensive evaluations of test results and targeted modification of the testing technology aimed to reduce the overall error. Random errors are calculated using absolute RMS deviations, while relative random error calculations seem far more reasonable. This article provides formulas for such calculations. It is advisable to combine the initial data into a single table, the format for which is suggested in the article. Sampling point calculation uses certain information about the product tested, namely: the coefficient of variation per shift (batch), the sample preparation procedure, assay subsample data, and the relative error for the measurementtechnique applied. A procedure is shown for establishing the coefficients of variation and the measurement technique error at an operating processing plant using routine testing data. A copper-zinc ore processing circuit, typical for the processing plants of the Urals, is used as an example for calculating random errors in the sampling of the original crushed ore, concentrate, and tailings. It is shown that the sampling error is critical when testing ore to establish the mass fraction of copper and the assay error produces the largest impact when establishing the mass fraction of gold. When sampling tailings and concentrate to determine the mass fraction of copper, sampling and assay errors make approximately equal contributions; when sampling to establish the mass fraction of gold, sample preparation and assay errors make a significant contribution. A comprehensive analysis of the impact produced by each sampling operation allows achieving the desired result in minimizing the random error.

keywords Testing of processing products, relative random error, coefficient of variation, sample preparation procedure, number of samples, error formula, calculation method

1. Gy P. Sampling of particulate material: Theory and practice. Amsterdam: Elsevier, 1982. 431 p.
2. Kozin V. Z. Testing of mineral raw materials. Ekaterinburg: USGU, 2011. 316 p.
3. Glazatov A. N., Tsemekhman L. Sh. Development of raw material and product sampling methods with determination of content of non-ferrous and precious metals at concentration and metallurgical enterprises. Part 1. Tsvetnye Metally. 2015. No. 10. pp. 54–59. DOI: 10.17580/tsm.2015.10.09.
4. Glazatov A. N., Tsemekhman L. Sh. Development of raw material and product sampling methods with determination of content of non-ferrous and precious metals at concentration and metallurgical enterprises. Part 2. Tsvetnye Metally. 2015. No. 12. pp. 18–24. DOI: 10.17580/tsm.2015.12.03.
5. Bondarenko A. V., Zakharov P. A., Shevelev E. S. Automatic pulp assay system for mining and processing industry. Gornyi Zhurnal. 2016. No. 11. pp. 75–79. DOI: 10.17580/gzh.2016.11.14.
6. Nikitenko E. M., Evtushenko M. B., Yushina T. I. Improving the assay test for the Degdekan deposit ores. Obogashchenie Rud. 2019. No. 1. pp. 34–38. DOI: 10.17580/or.2019.01.05.
7. Engström K., Esbensen K. H. Evaluation of sampling systems in iron ore concentrating and pelletizing processes — quantification of total sampling error (TSE) vs. process variation. Minerals Engineering. 2018. Vol. 116. pp. 203–208.
8. Lotter N. O., Evans C. L., Engström K. Sampling — a key tool in modern process mineralogy. Minerals Engineering. 2018. Vol. 116. pp. 196–202.
9. Napier-Munn T. J., Whiten W. J., Faramarzi F. Bias in manual sampling of rock particles. Minerals Engineering. 2020. Vol. 153. DOI: 10.1016/j.mineng.2020.106260.
10. Gleeson D. Getting to the core. International Mining. 2019. February. pp. 64–68.
11. Rozendal A., Le Rous S. G., du Plessis A., Philander C. Grade and product quality control by microCT scanning of the world class Namakwa Sands Ti-Zr placer deposit West Coast, South Africa: An orientation study. Minerals Engineering. 2018. Vol. 116. pp. 152–162.
12. Svensmark B. Extensions to the theory of sampling 1. The extended Gy's formula, the segregation paradox and the fundamental sampling uncertainty (FSU). Analytica Chimica Acta. 2021. Vol. 1187. DOI: 10.1016/j.aca.2021.339127.
13. Komlev A. S. Combined method of sampling and reduction of samples of mineral products. Ekaterinburg: Fort Dialog-Iset', 2020. 216 p.
14. Verkhozin S. S. OLGA: in-line gold analyzer Gekko Systems. Zolotodobycha. 2021. No. 10. URL:

Language of full-text russian
Full content Buy