$$ \gamma(h) = \frac{1}{2N(h)} \sum_{i=1}^{N(h)} [Z(x_i) - Z(x_i + h)]^2 $$
$$ R(t) = R_{max} \cdot \frac{t^n}{K^n + t^n} $$
Modern mineral engineering is no longer about "the best guess of the chief metallurgist." It is about probabilistic forecasting , quantified risk , and data-driven optimization . Engineers who ignore statistics are not practicing engineering; they are gambling. Those who master the variogram, Gy’s formula, and Bayesian updating will be the ones who unlock value from complex orebodies in a volatile commodity market. Statistical Methods For Mineral Engineers
$$ \sigma^2_{FSE} = \frac{1}{M_S} \left( \frac{f g \beta d^3}{c} \right) $$
Where $p$ is the probability of recovery (the metal reporting to concentrate). Many flotation recovery curves follow a sigmoidal shape. The Hill equation (borrowed from biochemistry) models recovery as a function of residence time: $$ \sigma^2_{FSE} = \frac{1}{M_S} \left( \frac{f g \beta
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. $200g \times 2,350,000 = 470,000 kg$.
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. The grind size is $P_{80} = 75 \mu m$
Where $\gamma(h)$ is the semivariance, $h$ is the lag distance, and $Z$ is the grade.