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Measuring sampling fairness and geochemical consensus for blasthole assays within grade-block mining units




Selective mining units, grade-blocks, sampling fairness, geochemical consensus, robust estimator, high breakdown, statistical outliers


In the mining industry, current grade control practices lack a standardised framework that can assess the reliability of average grade estimates computed for selective mining units (otherwise known as grade-blocks) within a mining bench. This article describes two measures that can quantify sampling fairness and geochemical consensus. Concretely, sampling fairness considers spatial factors such as sampling density and bias in the spatial distribution of blastholes whereas geochemical consensus considers the agreement between the assay samples within a grade-block. Geochemical disparity is measured using a robust distance estimator and a masking formula that takes into account the proportion of outliers and magnitude of differences observed above a threshold. The efficacy of the consensus measure is demonstrated through validation experiments. The results confirm the MCD robust estimator can breakdown when the fraction of outliers exceeds (n−k−1)/(2n). For k ≥ 2 variables and a sample size n≥10, this typically leads to an underestimation of the true extent and impact of outliers when they exceed 40%. An extension based on split-sequence analysis is proposed to overcome this limitation. The method is evaluated using production data from an open-pit iron ore deposit. An open-source implementation of the proposed algorithms will be available on GitHub.


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