Statistical Methods For Mineral Engineers Guide
A allows the engineer to estimate main effects and interactions with minimal tests.
You are designing a sampling protocol for a leach feed. The grind size is $P_{80} = 75 \mu m$. You take a 200g pulp for analysis. The variance is acceptable. Now you need to sample crushed ore at $P_{80} = 10mm$ (10,000 $\mu m$). The particle size ratio is $10,000 / 75 = 133$. The mass required must increase by $133^3 \approx 2.35 \text{ million}$ times. $200g \times 2,350,000 = 470,000 kg$. Statistical Methods For Mineral Engineers
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). A allows the engineer to estimate main effects
$$ R(t) = R_{max} \cdot \frac{t^n}{K^n + t^n} $$ You take a 200g pulp for analysis
Where $\gamma(h)$ is the semivariance, $h$ is the lag distance, and $Z$ is the grade.
A copper porphyry deposit. Inverse distance weighting might over-weight a single high-grade assay near a fault. Kriging detects the anisotropy (directionality) and assigns weights based on the continuity along the ore body vs. across it. Part 3: Sampling Theory – Gy’s Formula Pierre Gy dedicated his life to the statistics of sampling. His fundamental law is that the sampling variance (apart from geological variance) is inversely proportional to the sample mass.
$$ \ln\left(\frac{p}{1-p}\right) = \beta_0 + \beta_1 X_1 + ... + \beta_n X_n $$