Where $\gamma(h)$ is the semivariance, $h$ is the lag distance, and $Z$ is the grade.
$$ (X - \hat{X})^T V^{-1} (X - \hat{X}) $$ Statistical Methods For Mineral Engineers
Low-precision measurements (e.g., a problematic conveyor scale) get adjusted more than high-precision measurements (e.g., a calibrated lab balance). The output is a single, coherent set of production data. Part 6: Regression Analysis for Recovery Optimization Linear regression is the workhorse, but mineral processes are rarely linear. Logistic Regression Recovery is a proportion between 0 and 1. Linear regression can predict values outside this range ($>100%$). Logistic regression models the log-odds of recovery: Where $\gamma(h)$ is the semivariance, $h$ is the
If $X$ is the vector of measured variables and $V$ is the variance-covariance matrix of measurements, we find the adjusted values $\hat{X}$ that minimize: Part 6: Regression Analysis for Recovery Optimization Linear
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:
Statistically, we have redundant data. You have 3 assays (Feed, Con, Tail) and 2 flow rates (Feed, Tail). The system is over-determined . Modern metallurgical accounting uses minimization of weighted sum of squares to adjust measurements so they obey the conservation of mass (tonnage and metal).
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).