485 the variability in feed, throughput, mineralogy, circuit conditions etc., it was extremely difficult to visually isolate the impact of the unit upon overall recovery. However, this was easily overcome with analysis using a paired t-test, which can be performed in Microsoft Excel (Table 1). Table 1 – Microsoft Excel paired t-test output. Rec (%) - ON Rec (%) - OFF Mean 88.6 87.3 Variance 6.4 4.8 Observations (no. of pairs) 30 30 df 29 t Stat 4.0 P 0.00018 The mean recovery difference between the ON and OFF conditions was 88.6% - 87.3% = 1.3% recovery. Whether this 1.3% recovery benefit was indeed ‘real’ is answered by the P-value in the final row of Table . The level of confidence that the result was statistically significant is given by 100(1-P) = 99.98%. In other words, there was over 99% confidence that the flash flotation unit provided a real metallurgical recovery improvement when it was switched on, and that the observed mean 1.3% recovery change was not simply an artefact of experimental error. This was reinforced by the 95% confidence intervals on this improvement, ± 0.7% recovery4. This equated to an additional $6.3 M USD per year of revenue. Given that the recovery improvement was swamped by the range in recovery data (D12% in this instance), it would have otherwise been impossible to quantify this benefit without a structured experimental trial, formally designed according to statistical criteria. The production team subsequently decided to keep the unit on, while investing in upgrades of ancillary equipment to improve its operability. In a conventional paired trial, the required length of trial (sample size) is determined prior to the commencement of the experiment, which is then run for this entire duration to ensure the integrity of the statistical outputs. A modification of traditional paired analysis is described in Vizcarra et al. (2023) which allows for the possible termination of the trial prior to the duration prescribed by traditional sample-size formulas. Significant reductions in trial length, often in the order of ~50%, were reported while maintaining the same degree of risk-control as conventional paired testing and analysis. This approach streamlines the execution of paired-trials, allowing operations to make good decisions in circumstances where time is of the essence. 3. OPTIMISING GRIND SIZE WITHOUT CAPITAL EXPENDITURE USING CCRDS Mineral concentrators are comprised of complex, multi-variable processes, where the best combination of set-points is often debated within production teams. A classic approach to identifying these is to test one-variable at a time, while holding other variables constant. Such experiments, however, are timeconsuming, inefficient, cannot detect factor interaction, and frequently fail to identify process optima. An experimental design called a Central Composite Rotatable Design (CCRD) overcomes these difficulties by (counter-intuitively) allowing for the testing of multiple variables simultaneously. CCRDs are discussed in detail in Napier-Munn (2014). They prescribe specific set-point combinations of the manipulated variables according to the schematic shown in Figure . This enables the concurrent testing of multiple process variables, thereby reducing the size of the experiment, while also enabling the effect of these variables to be established through the inherent process ‘noise’ that would otherwise overwhelm the results of an ad-hoc plant trial. 4 Calculated by ± Mj,/√Å where t (0.05, 29) = 2 for 29 degrees of freedom, sd (sd of paried differences) = 1.8%, and n (number of pairs) = 30.
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