Mineral Engineers — Statistical Methods For

$$ \gamma(h) = \frac{1}{2N(h)} \sum_{i=1}^{N(h)} [Z(x_i) - Z(x_i + h)]^2 $$

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:

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). Statistical Methods For Mineral Engineers

In the world of mineral engineering, decisions have billion-dollar consequences. A mill that operates at 85% recovery instead of 90% can render a deposit uneconomical. A misinterpreted assay grid can lead to the development of a barren hill. Unlike chemical engineering (which deals with pure reactants) or mechanical engineering (which deals with deterministic tolerances), mineral engineering must contend with heterogeneity .

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: A misinterpreted assay grid can lead to the

A allows the engineer to estimate main effects and interactions with minimal tests.

For mineral engineers, this is revolutionary. Low-precision measurements (e.g.

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: