Provide quick visual checks for correlations between variables, such as reagent dosage versus rougher recovery. 3. Inferential Statistics and Hypothesis Testing
: Proper setup of laboratory and plant-scale trials.
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.
Ms=c⋅⋅f⋅g⋅d3sFSE2cap M sub s equals the fraction with numerator c center dot center dot f center dot g center dot d cubed and denominator s sub cap F cap S cap E end-sub squared end-fraction = Mineralogical composition factor = Liberation factor = Particle shape factor = Size distribution factor = Top size of the particles (nominal maximum size) 3. Hypothesis Testing and Process Comparisons Statistical Methods For Mineral Engineers
For those looking for a physical or digital copy, it is published by at the University of Queensland and is frequently used as the primary text for their professional development courses.
A processing plant can never be optimized if its basic production numbers are inaccurate. Raw plant measurements (flow rates, assays, densities) never perfectly balance due to measurement errors, spillage, and sensor drift. Data Reconciliation and Mass Balancing
A copper-molybdenum plant used a ( 2^3 ) factorial design and discovered that the interaction between collector dosage and pH was statistically significant (p < 0.01), whereas neither factor alone was significant. The optimum was found at a combination previously dismissed by OFAT trials. Modern practice uses weighted least squares, where each
Many mineral processes exhibit cycles: trommel screen blinding, flotation froth collapse cycles, or shift-change effects. Spectral analysis (Fourier transform) identifies hidden frequencies. For example, a 24-hour cycle in plant feed density might indicate a change in mine haulage patterns rather than a process problem.
Applies to stable, controlled process variables like target grind sizes or steady-state chemical additions.
Constructs equations to forecast recovery and grade based on feed inputs. Laboratory and Pilot Optimization Hypothesis Testing and Process Comparisons For those looking
In modern mineral processing and mining operations, efficiency is no longer just about mechanical reliability; it is about data utilization. Mineral engineers manage complex, inherently variable systems where small improvements in recovery or grade yield millions of dollars in revenue. Statistical methods provide the mathematical framework required to transform noisy plant data into actionable operational decisions, ensuring rigorous quality control, accurate forecasting, and process optimization. 1. Introduction to Data Variability in Mineral Processing
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.
The probability of obtaining the observed results if the null hypothesis is true. A p-value below a threshold (typically 0.05) justifies rejecting H0cap H sub 0 Type I Error (
A statistical analysis is only as good as the physical sample collected. In mineral processing, heterogeneous ore bodies make unbiased sampling exceptionally difficult. Pierre Gy’s Sampling Theory