Conclusion: You cannot accurately sample coarse material with small masses. This explains why "scoop sampling" of conveyors is fundamentally flawed without proper mass reduction protocols (riffle splitters, rotary dividers). Once the mine feeds the plant, the mineral engineer shifts from geology to metallurgy. Here, Statistical Process Control (SPC) is the standard. The Moving Range Chart Most mineral processes have autocorrelation (tonnage now depends on tonnage 5 minutes ago). Traditional X-bar-R charts are less useful; Exponentially Weighted Moving Average (EWMA) charts are superior because they detect small, persistent shifts. Design of Experiments (DOE) Classical "one factor at a time" (OFAT) testing is statistically inefficient. Mineral engineers often face interactions (e.g., pH and collector dosage interact to affect recovery).
$$ (X - \hat{X})^T V^{-1} (X - \hat{X}) $$ Statistical Methods For Mineral Engineers
$$ \ln\left(\frac{p}{1-p}\right) = \beta_0 + \beta_1 X_1 + ... + \beta_n X_n $$ Here, Statistical Process Control (SPC) is the standard
Where $\gamma(h)$ is the semivariance, $h$ is the lag distance, and $Z$ is the grade. Design of Experiments (DOE) Classical "one factor at
$$ \sigma^2_{FSE} = \frac{1}{M_S} \left( \frac{f g \beta d^3}{c} \right) $$
Gy’s Formula for Fundamental Sampling Error: