STATISTICS AND SPLITTING LIMITS Review of Au Fire Assay

Transcription

1 STATISTICS AND SPLITTING LIMITS Review of Au Fire Assay JONATHAN FORREST RCM MICHAEL W. HINDS RCM MADELEINE THERON -RAND REFINERY REVIEW OF SPLITTING LIMITS Refiner and Clients each compare assay values for settlement If the results are within an agreed upon difference (the splitting limit) : Average of two results is calculated for settlement. Original refiner assay is accepted Other calculations depending on contract and material If the difference greater than the splitting limit then it can be settled by an umpire lab assay. Over the past few years, we have observed the requests to have the splitting limit reduced. 2 Session 7 Forrest 1

2 REDUCED SPLITTING LIMITS Splitting limit of 0.1% or 1 is typically used for gold doré between refiner and clients (from informal discussions) Same for different Au concentration levels Uncertainty increases with lower Au concentration Over the past few years some clients have been asking for lower splitting limits below 0.8 In some cases, a lower splitting limit will mean going to umpire over differences that are not statistically significantly different (or analytically the same). Unnecessary umpire analyses and expenses Delays in settlement WHY THE MOVE TO LOWER SPLITTING LIMITS? Price of Gold Cost of Production Increasing Refining Charges Increasing New Personnel Limited by: Homogeneity of the Material Assay Uncertainties Gold Concentration Sampling Methods 4 Session 7 Forrest 2

3 DIFFERENCE BETWEEN ASSAY A AND ASSAY B SIGNIFICANT? Frequency Au Concentration, SPLITTING LIMIT FOR A HOMOGENEOUS MATERIAL PROFICIENCY TEST MATERIAL Very Homogeneous Sample Standard Deviation a Reflection of Homogeneity Assay Uncertainty From 2014 LBMA Proficiency Test Sample Au concentration = ± replicates Use Student s t-test to determine what significant difference can be measured. 6 Session 7 Forrest 3

4 REARRANGEMENT OF STUDENT S t - test t calc ( x x ) s (1/ n 1/ n ) x1 x2 t tab s (1/ n 1) (1/ n 2) Where: x 1 x 2 a significant difference between to averages or splitting limit n 1 and n 2 number of replicates for averages s = standard deviation; assume same for both averages t calc = t tab at point of significant difference (see t-table for values) 7 STUDENT S t Table Degrees of Freedom (n-1) t 95% confidence interval Adapted from Neave, N.R., Elementary Statistics Session 7 Forrest 4

5 CALCULATION OF SPLITTING LIMIT (Significant Difference) Homogeneous Sample Assumptions for the calculation: 1) n 1 = n 2 = 4 replicates or 3 degrees of freedom 95% confidence t tab = ) standard deviation s = 0.05 x x t s (1/ n ) (1/ n ) x x tab x 3.18(0.05 ) (1/ 4) (1/ 4)) x 0.11 Splitting limit of is more realistic with this material UNCERTAINTY WITH CHANGES IN AU FOR DEPOSITS FROM ONE REFINER Concentration Au in Deposits Expanded Uncertainties k=2 > Session 7 Forrest 5

6 MORE REALISTIC EXAMPLE A client s gold dorè has the following composition: Au 700 Ag 100 Base metals 20 In general, the standard deviation of the Au concentration determined by fire assay is estimated to be ± 0.4 The client wants a 0.6 splitting limit Is this reasonable? CALCULATION OF SPLITTING LIMIT (Significant Difference) Less Homogeneous Sample Assumptions for the calculation: 1) n 1 = n 2 = 4 replicates or 3 degrees of freedom 95% confidence t tab = ) standard deviation, s = 0.4 x x t s (1/ n ) (1/ n ) x x tab x 3.18(0.4 ) (1/ 4) (1/ 4)) x 0.9 Splitting limit of 0.6 should NOT be used for this material Session 7 Forrest 6

7 EFFECT OF INHOMOGENEITY EXPRESSED AS STANDARD DEVIATION n = 4, t = 3.18 Standard Deviation Significant Difference EFFECT OF NUMBER OF REPLICATES Standard Deviation n t Significant Difference Increasing the number of replicates lowers the significant difference As replicates increase the amount of change decreases The cost of having more replicates must also be considered Session 7 Forrest 7

8 SIGNIFICANT DIFFERENCE VS SPLITTING LIMIT Significant Difference calculated for a set standard deviation Standard Deviations noted are typical Estimated median or calculated pooled standard deviation from many assays Sometimes higher or lower Significant Difference varies with standard deviation Splitting Limit calculated from significant difference: Minimum Limited by standard deviation Best to calculate significant differences for a range of standard deviations to see what will work to satisfy both client and refiner as a Splitting Limit FACTORS EFFECTING AGREEMENT IN FIRE ASSAY BETWEEN REFINER, CLIENT, & UMPIRE Number of Sample Replicates Sample Weight ASTM E1335: 0.5 g (gold doré) ISO 11426: g (Au in Jewellery Alloys) Observed clients use as low as 0.15 g (gold doré) Proof Correction Matrix Matching Difference between matching Au proof weight and using generic Au proof weight (0.5 g) can be 0.4 Number and Purity of Au Proofs Calculation of Proof Correction ASTM: proof ratio before and after ISO: subtract proof difference Very small difference 0.01 Session 7 Forrest 8

9 CONCLUSION Statistical method presented that will assist in evaluating whether the splitting limit is reasonable in view of the homogeneity of the material May take time to gather this information Best agreement, when client and refiner laboratories use the same: Sample weight Number of replicates Proof correction method and number of proofs Calculation method ACKNOWLEDGEMENTS Rand Refinery Pty (Ltd) Royal Canadian Mint Neil Harby, LBMA 18 Session 7 Forrest 9