Sampling density and grade control

In open pit mining, each small mining unit (SMU) is selected for mill processing based on an estimate of its true grade. The estimation is usually done using analyses of cuttings from blast holes within that SMU. One common estimator used for selection is the arithmetic average of within-SMU samples. This estimator is conditionally biased. The effect of a conditional bias is to overestimate the profit really recovered from the deposit. For this reason, a conditionally unbiased estimator is preferable. Increasing the number of samples generally improves the accuracy of the estimation (and diminishes the conditional bias, if present, of most estimators). However, there exists a practical limit where an additional sample does not improve the estimation sufficiently to cover the expense of making the analysis. This limit is specific to each deposit and depends on geostatistical parameters, economic factors, and mining parameters. This study examines how the number of samples affects the recovered reserves and the resulting profit. Also, the effects on optimal profit of varying the different factors are examined. Globally, the number of samples required increases with the selectivity of the operation. For a given ore deposit, the greater the number of SMUs selected for processing, the fewer samples are required and vice-versa.