A copper-molybdenum plant used a ( 2^3 ) factorial design and discovered that the interaction between collector dosage and pH was statistically significant (p < 0.01), whereas neither factor alone was significant. The optimum was found at a combination previously dismissed by OFAT trials. 3.2 Response Surface Methodology (RSM) Once significant factors are identified, RSM (e.g., Central Composite Design, Box-Behnken) models curvature. This is essential for finding true maxima (recovery) or minima (cost, reagent consumption).
From the first drill core to the final concentrate shipment, every decision involves sampling error, process variability, and uncertainty. Mastering the statistical methods outlined above transforms a mineral engineer from a reactive troubleshooting into a proactive optimizer. Statistical Methods For Mineral Engineers
Introduction: Why Statistics Matter in Mineral Engineering For decades, mineral engineering was dominated by empirical rules of thumb, metallurgical “balance” calculations, and deterministic models. A plant metallurgist would take a grab sample, run a quick assay, and adjust the flotation pH based on instinct. While experience remains invaluable, the modern mining industry has realized a hard truth: mineral variability is the only constant. A copper-molybdenum plant used a ( 2^3 )
A reconciled feed grade that is statistically more reliable than any single direct measurement. Part 6: Advanced Methods – Multivariate Statistics Today’s mineral engineer has access to automated mineralogy (QEMSCAN, MLA), NIR sensors, and laser diffraction. This creates high-dimensional data. 6.1 Principal Component Analysis (PCA) PCA reduces dozens of variables (e.g., particle size bins, mineral abundance, XRD peaks) into a few uncorrelated “principal components.” This is essential for finding true maxima (recovery)
[ s^2 = K \cdot d^3 \cdot \left( \frac1M_L - \frac1M_T \right) ]
A plant processing a complex sulfide ore used PCA on 25 QA/QC variables. Two components explained 78% of variance: PC1 (sulfide content) and PC2 (clay content). Monitoring just these two components instead of 25 separate charts simplified control. 6.2 Partial Least Squares (PLS) for Grade Prediction PLS is ideal when you have many collinear predictors (e.g., XRF elemental intensities) and want to predict an assayed grade. PLS finds latent variables that maximize covariance between predictors and responses.