Correction factor to the formula of sample reduction error

Abstract

Introduction. Theoretical results have been obtained that allow calculating random sampling errors. One of the main calculation formulas for determining the sampling error is the sample reduction error formula. The sampling errors determined by this formula differ from the errors determined experimentally. The sample reduction error consists of several components, a separate quantitative determination of which is necessary when developing methodological support for testing processes. It is impossible to determine all these components separately from each other experimentally. It is necessary to determine the ratio of the components of the specified formula. Methods of research. The sample reduction error, determined analytically, is the minimum possible reduction error when this operation is ideally performed. To take into account the deviation from the ideal conditions for performing the reduction operation, it is necessary to experimentally estimate the amount of the actual deviation and link it with the theoretical result. As a result, the value of the correction factor can be obtained, which should be entered into the formula for calculating the reduction error. In order to eliminate the need for experimental determination of the error of the method of measuring the mass fraction, experiments to determine the correction factor should be performed on artificial samples with markers. Research procedure. Experiments were performed to reduce samples with markers. 480 reductions of the same sample were performed, which showed the coincidence of the theoretical and experimental distributions of the number of markers in the reduced samples. The correction factor in the experiment with markers of the correct shape was 1.3. The same coefficient in the experiment with markers whose granulometric composition match with that of the sample material was 2.0. The average value of the correction factor in reproducibility conditions was 2.13. Results and analysis. As a result of two experiments on multiple reduction of the sample, it was found that the correction factor under reproducibility conditions should be within 1.3 and 2.0. Similar information about the differences in reproducibility and repeatability errors in international and Russian standards shows that in order to move from a theoretical formula to a real reproducibility error, a correction factor from 2.0 to 3.0 should be introduced. Conclusions. The introduction of correction coefficients into the reduction error formula makes it possible to calculate the real errors of sample reduction, as well as quantify the results of mineral products testing based on the calculation.