Statistical tools, including dynamic time warping (DTW) , are used to compare yield-ash curves. This numerical comparison helps validate coal cleaning performance across different testing protocols. 4. Conclusion
Weeks later, the company faced a decision: expand the pit now, risking early capital for uncertain high-grade pockets, or stage expansion after additional drilling. The board asked for a recommendation. Amaya prepared a concise report: maps showing kriged grade means, probability maps from simulations, sensitivity analysis of recoverable metal under different cut-offs, and the economics under several scenarios. She highlighted blocks with high probability of exceeding cutoff but high conditional variance — the places where an extra drill hole would most reduce uncertainty.
Before applying complex models, data must be understood through descriptive statistics.
The text is structured as a "how-to" manual rather than a dense academic tome: Statistical Methods For Mineral Engineers
| Tool | Mineral Engineering Application | Why Interesting | |------|--------------------------------|------------------| | | Real-time smoothing of XRF assay streams | Filters out high-frequency noise to show true trend. | | Control Charts (Shewhart) | Monitoring mill power draw, density, pH | Detects special-cause variation before a spill or crusher jam. | | Linear Regression | Relating Bond Work Index to throughput | “For every 1 kWh/t increase in Wi, throughput drops 12 t/h.” | | Monte Carlo Simulation | Predicting monthly metal production given grade and recovery uncertainty | Turns “maybe 10,000 oz” into “10% chance <9,200 oz, 50% chance ~10,500 oz.” | | Taguchi Methods | Designing a flotation reagent dosage experiment with minimal tests | 8 experiments instead of 81 – finds optimum without bankrupting the lab. |
Once the critical variables are identified, RSM is used to map the mathematical space and locate the absolute optimum operational settings.
Statistically, we have redundant data. You have 3 assays (Feed, Con, Tail) and 2 flow rates (Feed, Tail). The system is over-determined . Statistical tools, including dynamic time warping (DTW) ,
When comparing multiple variables simultaneously—such as evaluating gold extraction across four different cyanide concentrations across three distinct ore blocks—ANOVA separates true process improvements from random operational noise. 5. Regression Analysis and Empirical Modeling
| Hour | Head Grade (% Cu) | Tails Grade (% Cu) | |------|------------------|--------------------| | 6 AM | 0.95 | 0.08 | | 7 AM | 0.88 | 0.09 | | 8 AM | 0.97 | 0.14 |
: A method to reduce the influence of known but uncontrollable variables (like ore hardness variations over time) on trial results. Response Surface Methodology (RSM) Conclusion Weeks later, the company faced a decision:
Rather than changing one factor at a time (OFAT), modern mineral engineering uses design of experiments to study multiple factors efficiently.
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).