These errors occur due to the physical design of the sampling equipment and can be eliminated through proper engineering.
Compares the means of two groups. A paired t-test evaluates the same circuit before and after a specific change (e.g., changing a frother type). An independent t-test compares two parallel flotation banks running different reagents.
Measures the spread of data points around the mean, serving as a critical input for process capability studies. Data Distributions
Experienced practitioners therefore ensure that their geological model meets expectations for deposit formation under the prevailing conditions of mineralisation. Grade distributions themselves often record the structural architecture of mineral systems – folds, shears, faults, and lithological contacts can be detected directly from drill‑hole assays, providing valuable constraints before any statistical estimation begins. The most reliable statistical models are those built on a foundation of sound geological understanding.
When formulating a collector blend (e.g., xanthate + dithiophosphate + mercaptan), the proportions sum to 100%. Standard factorial designs fail here. Mixture designs (simplex lattice, extreme vertices) are required. They model synergistic and antagonistic effects correctly. Statistical Methods For Mineral Engineers
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.
standard deviations). They allow operators to identify assignable causes of process drift before the plant produces off-specification concentrate. 3. Mass Balancing and Data Reconciliation
Statistical methods, however sophisticated, cannot compensate for an incorrect geological model. Industry evidence shows that many resource downgrades stem not from sampling or geostatistical errors but from incorrect domain geometry, unrealistic continuity assumptions, and implicit modelling artefacts. The underlying principle – “structure before statistics” – is worth repeating: statistical estimation within domains is typically robust, but errors introduced during geological interpretation propagate directly into tonnage and grade outcomes.
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. These errors occur due to the physical design
Identifies the middle value, providing a measure of central tendency less affected by extreme assay outliers.
A copper deposit has a mean grade of 0.8% Cu and a CV of 1.2. This implies the plant will frequently see grades from <0.2% to >2.0%. Blending from multiple stockpiles is essential.
Modern practice uses weighted least squares, where each measurement is assigned a variance (from sampling and analytical error). Measurements with low variance receive small adjustments; bad actors receive large adjustments—flagging them for review.
CF=f−tc−tthe fraction with numerator cap C and denominator cap F end-fraction equals the fraction with numerator f minus t and denominator c minus t end-fraction Generalized Least Squares (GLS) Reconciliation An independent t-test compares two parallel flotation banks
Mean grade is deceptive in mineral processing because high-grade outliers can pull the arithmetic mean upward, while the median better represents what the plant actually sees.
The mean provides the baseline operational target, while the median offers a robust measure of central tendency less influenced by operational upsets or assay outliers.
Monitoring daily recovery, grind sizes, and thickener underflow
: Tim Napier-Munn’s 50 years of industry experience, including co-authoring the famous Wills' Mineral Processing Technology , lends the book significant professional weight.
Once DoE has identified the critical factors, RSM is a collection of mathematical and statistical techniques used to model and optimize the response. In the context of flotation, RSM would create a regression model relating the input factors (e.g., frother dosage, air flow rate) to the output responses (e.g., copper recovery, concentrate grade). The goal is to find the combination of factors that maximizes a desired response, such as economic recovery.