Statistical Methods For Mineral Engineers -

greater than 1.33 indicates a highly capable, statistically stable process.

“You taught us the math and the models,” Lin said. “But more than that — you taught us to treat uncertainty like information, not an obstacle.”

Mean, median, and mode. The median is critical when dealing with skewed environmental or assay data containing extreme outliers.

: Used for comparing quantities and determining if differences in performance (e.g., between two circuit configurations) are statistically significant. Analysis of Variance (ANOVA)

Industrial plants cannot measure every flow rate or stream grade directly due to physical constraints and instrument costs. Mass balancing mathematically reconciles contradictory raw data to satisfy the law of conservation of mass. Two-Product Formula For a simple separation circuit with a feed ( ), concentrate ( ), and tailings ( ) stream, and their respective grades ( ), the mass balance is defined by: F=C+Tcap F equals cap C plus cap T Statistical Methods For Mineral Engineers

Highly sensitive to small, persistent shifts in the process mean. CUSUM charts are ideal for detecting gradual changes, such as the slow degradation of grinding media or subtle shifts in ore hardness.

Shewhart, CUSUM, and EWMA charts track process stability over time. For example, a shift in a grinding mill's power draw chart can give early warning of liner wear or feed size changes.

Examining the combined effect of multiple variables (e.g., reagent dosage + grind size + pH).

SME-STAT-2025-04 Target Audience: Plant Metallurgists, Mine Geologists, Process Engineers Core Message: In a world of inherently variable ore, statistics is not just about averages—it’s the science of making confident decisions despite chaos. greater than 1

A plant using kriged block models instead of inverse-distance weighting reduced flotation feed grade swings by 40%, stabilizing reagent consumption.

Run a fraction of the full design when testing costs or time are prohibitive, accepting some loss of higher-order interaction data. Optimization and Response Surface Methodology (RSM)

Monitoring product quality and tailings losses in real-time.

are the mass flow rates of Feed, Concentrate, and Tailing, and are their respective assays. Weighted Least Squares (WLS) Adjustment The median is critical when dealing with skewed

Kriging is the general name for a family of generalised least-squares regression algorithms that use the variogram to assign weights to neighbouring samples for grade estimation at unsampled locations. Ordinary kriging (the most widely applied form) assumes a constant but unknown mean within each estimation domain. The kriging variance – a measure of estimation uncertainty – is produced alongside each grade estimate, providing a quantitative indicator of confidence.

: Comparing timed mean grade/recovery curves and performing regression analysis to establish relationships between variables.

The primary crusher gap had drifted open over the weekend, producing coarser feed. Flotation kinetics slowed.

Statistical methods provide the mathematical framework required to transform noisy plant data into actionable operational insights. By applying these techniques, engineers can quantify uncertainty, optimize recovery rates, and minimize resource waste. 1. Sampling Theory and Variance Control

The students watched as statistics moved from abstraction to consequence. One night, a younger engineer named Mateo asked, “Which method is right? Kriging, simulation, indicator—how do we pick?”