PCA reduces the dimensionality of massive plant datasets. It compresses dozens of correlated sensor readings (pressures, flows, power draws) into a few orthogonal "Principal Components," making it much easier to visualize day-to-day operational drift. Partial Least Squares (PLS)
Never trust an assay result without knowing how the sample was collected, crushed, and split. A statistically invalid sample is worse than no sample—it leads to wrong decisions with false confidence.
Minimize J=∑i=1n(xi−x̂iσi)2Minimize cap J equals sum from i equals 1 to n of open paren the fraction with numerator x sub i minus x hat sub i and denominator sigma sub i end-fraction close paren squared Subject to the conservation of mass constraints: ∑Mass In=∑Mass Outsum of Mass In equals sum of Mass Out = Measured value (e.g., feed assay) x̂ix hat sub i = Reconciled estimate σisigma sub i = Standard deviation of the sensor/assay method
The objective of grade control is to accurately delineate ore and waste at the mine face to ensure what is sent to the mill matches the resource model. This is a blending and management problem deeply rooted in statistics. Tools such as moving averages are used to smooth out local variability in blast hole assays. More advanced techniques, such as the Nachman model , are applied in diamond mining to relate the mean population density to the proportion of barren samples, helping to establish reliable grade estimates in sparse, high-value deposits. The use of blast hole data is notoriously noisy; applying geostatistical filtering techniques helps to separate the "signal" (the real grade trend) from the "noise" (the small-scale variability), leading to more efficient ore-waste boundaries.
: A collection of mathematical and statistical techniques used to model and optimize processes, such as finding the temperature and pressure that maximize yield. 3. Monitoring Plant Trials
Unlike laboratory experiments, plant data is autocorrelated: today’s feed grade is correlated with yesterday’s. Standard t-tests or regression (which assume independence) give misleading p-values.
Mineral engineers use specific statistical tests to compare data sets and validate results from plant trials: t-tests, F-tests, and Chi-square tests
Just as in any manufacturing process, SPC is used to monitor and control mineral processing operations. Traditional univariate charts (e.g., Shewhart, CUSUM) can track individual variables like pH or throughput to ensure they remain within statistically defined control limits. A more advanced approach, Multivariate Statistical Process Control (MSPC) , is increasingly favored in mineral processing. It can monitor dozens of process variables simultaneously. Using a method like Principal Component Analysis (PCA), MSPC creates a model of normal operation. Deviations are then detected using two powerful statistics: