Statistical Methods For Mineral Engineers -

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

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: Statistical Methods For Mineral Engineers

Where $\gamma(h)$ is the semivariance, $h$ is the lag distance, and $Z$ is the grade. A allows the engineer to estimate main effects

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). You have 3 assays (Feed, Con, Tail) and

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:

For mineral engineers, this is revolutionary.

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: