Operational data frequently contains anomalies caused by instrument calibrations, power surges, or slurry spills.
Modern concentrators generate thousands of data points every second via online analyzers, particle size monitors, and smart sensors. Univariate statistics cannot handle this dimensionality, necessitating multivariate techniques. Principal Component Analysis (PCA)
Used to model simple relationships, such as how increased collector dosage affects flotation recovery.
These metrics quantify how well a circuit meets operational specifications. A Cpkcap C sub p k end-sub Statistical Methods For Mineral Engineers
The digital revolution has brought ML into mainstream mineral processing. ML models, such as Random Forests and Support Vector Machines, are particularly powerful for handling complex, non-linear systems. One common use is for data reconciliation , where ML algorithms are used to clean and impute missing or erroneous data from plant sensors. Another is for predicting key performance indicators (KPIs) in real-time, enabling "soft sensors" to predict a critical variable (e.g., concentrate grade) that is otherwise difficult or expensive to measure directly.
ANOVA is a statistical workhorse used to test whether there are significant differences between the means of three or more groups. In mineral processing, it is commonly applied to compare the performance of different processing circuits, reagents, or operating shifts. For instance, an ANOVA can determine if the recovery from three different flotation collectors is statistically different or if the observed differences are merely due to random variation.
Statistical rigor requires appropriate tools. Spreadsheet software (Excel) is insufficient for advanced methods. Mineral engineers should be proficient in: Principal Component Analysis (PCA) Used to model simple
PCA reduces dozens of variables (e.g., particle size bins, mineral abundance, XRD peaks) into a few uncorrelated “principal components.”
: It contains over 100 Excel and Minitab hints and comes with downloadable example spreadsheets, making it highly actionable for immediate site use.
In a running processing plant, physical measurements rarely balance perfectly due to sensor inaccuracies, pipe scaling, and sampling errors. Mass balancing is the statistical process of adjusting raw plant measurements so they align with the fundamental law of conservation of mass. Weighted Least Squares (WLS) ML models, such as Random Forests and Support
: Understanding and quantifying the uncertainty inherent in measurement and sampling.
Statistical methods are not confined to the resource estimation phase; they are critical for day-to-day operations and quality management.
6. Design of Experiments (DoE) and Response Surface Methodology
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