Statistical Methods For Mineral Engineers [exclusive] May 2026

Statistical Methods for Mineral Engineers: A Practical Guide to Data-Driven Decision Making

Mineral engineering is inherently a discipline of uncertainty. Unlike manufacturing, where raw materials are consistent, mining deals with natural deposits that vary wildly in grade, geometry, and geotechnical properties. Statistical methods provide the tools to quantify this uncertainty, optimize processes, and manage risk.

Here is a comprehensive overview of key statistical methods applicable to mineral engineering, categorized by their application.

Part 1: Foundational Concepts – Describing the Orebody

Before any processing occurs, the resource must be quantified. Traditional geostatistics (kriging, variograms) is a field unto itself, but here we focus on practical statistical descriptors.

Part 7: Common Pitfalls and How to Avoid Them

| Pitfall | Consequence | Statistical Remedy | | :--- | :--- | :--- | | Using mean instead of median | Overestimates plant feed grade | Report P50, P90, and mean. Use geometric mean for lognormal data. | | Ignoring nugget effect in variograms | Underestimates short-scale variability | Perform rigorous variography with lag spacing < 10m. | | Applying t-tests to autocorrelated data | Massive type I error (false positives) | Use time-series control charts or pre-whiten data. | | Overfitting with stepwise regression | Model fails on new data | Use cross-validation or regularization (LASSO, ridge). | | Pseudoreplication in flotation tests | Inflated degrees of freedom | A single cell with 5 assays is not 5 replicates. Average first, then test across true replicates. | Statistical Methods For Mineral Engineers

The Lognormal Distribution

Most mineral engineers learn about the "Normal" (Gaussian) distribution in school. In reality, ore grades almost never follow a normal distribution. High-grade outliers are rare, but they are massive. Low grades are common. This creates a lognormal distribution (the log of the grade is normally distributed).

• Implication: Using arithmetic means for lognormal data overestimates the typical value. The geometric mean is often a more robust estimator of central tendency for skewed grade data.

Part 6: Regression Analysis for Recovery Optimization

Linear regression is the workhorse, but mineral processes are rarely linear.

D. Sampling Theory (Gy’s Fundamentals)

No statistical method for mineral engineers is complete without addressing the fundamental error of sampling.

• Integration: The book integrates Pierre Gy’s sampling theory, teaching engineers how to calculate the "Fundamental Error" associated with a sample mass.
• Practical Output: This allows the engineer to determine the minimum sample mass required to achieve a specific level of confidence in the assay result, preventing decisions based on insufficient sample sizes.

Part 2: Geostatistics – The Spatial Dimension

Traditional statistics treats data points as independent. Geostatistics, founded by Georges Matheron based on Danie Krige’s work in the South African gold mines, acknowledges that samples close together are more similar than samples far apart. Statistical Methods for Mineral Engineers: A Practical Guide

Part 3: Sampling Theory – Gy’s Formula

Pierre Gy dedicated his life to the statistics of sampling. His fundamental law is that the sampling variance (apart from geological variance) is inversely proportional to the sample mass.

Gy’s Formula for Fundamental Sampling Error:

$$ \sigma^2_FSE = \frac1M_S \left( \fracf g \beta d^3c \right) $$

Where:

• $M_S$ = Mass of sample
• $d$ = Size of the top particles ($d_95$)

The Golden Rule for Mineral Engineers: For a given desired variance, if you double the particle size ($d$), you must increase the sample mass by 8 times ($2^3$).

Practical Application: You are designing a sampling protocol for a leach feed. The grind size is $P_80 = 75 \mu m$. You take a 200g pulp for analysis. The variance is acceptable. Now you need to sample crushed ore at $P_80 = 10mm$ (10,000 $\mu m$). The particle size ratio is $10,000 / 75 = 133$. The mass required must increase by $133^3 \approx 2.35 \text million$ times. $200g \times 2,350,000 = 470,000 kg$.

Conclusion: You cannot accurately sample coarse material with small masses. This explains why "scoop sampling" of conveyors is fundamentally flawed without proper mass reduction protocols (riffle splitters, rotary dividers).