Reference Materials Update

Transcription

1 Reference Materials Update Review of Statistical Analysis Mike Hinds, Royal Canadian Mint, Canada Dirk Hofmans, Umicore, Belgium Chen Jie, Great Wall Precious Metal Company, China Jonathan Jodry, MetalorTechnologies SA, Switzerland Hitoshi Kosai, Tanaka Kikinzoku Kogyo KK, Japan Stewart Murray, LBMA Consultant, UK Hiroshi Sawai, Tanaka Kikinzoku Kogyo KK, Japan Madeleine Theron, Rand Refinery, South Africa Neil Harby and Varsha Peiris, LBMA, UK

2 Current State of LBMA Reference Materials AuRM1 & 2 SOLD OUT! (Au %) AgRM1 & 2 SOLD OUT! (Ag %) AuRM3 12 units remaining (Au %) Need to Manufacture and Certify Replacements AuRM4 and AuRM5 (Au %) AgRM4 and AgRM5 (Ag %) Contract for manufacture should be awarded shortly Estimate RM s to be ready early to mid 2018 Page 2

3 Proposed Replacements; AuRM4 & AuRM5 Target Concentrations, ppm Page 3 Elements AuRM4 AuRM5 Ag Al As 20 Bi Ca 10 Cd 10 Co 10 Cr 10 Cu Fe In 10 Ir 10 Mg 10 Mn 10 Ni Pb Pd Pt Rh 10 Ru 10 Sb 20 Se Si Sn 10 Te Ti Zn 10 30

4 Proposed Replacements; AgRM4 & AgRM5 Target Concentrations, ppm Elements AgRM4 AgRM5 Al 10 As Au Bi Ca 10 Cd Co 10 Cr 10 Cu Fe In 10 Mg 10 Mn 10 Ni Pb Pd Pt Sb 20 Se Si Sn 10 Te Zn Page 4

5 TARGET CONCENTRATIONS Many elements have a high and a low concentration Cover lower and upper ranges that might be commonly found From survey in 2008, elements cover 70% of elements determined Selected elements have only one concentration (ie., Cd in AuRM4) Elements included to cover list in LBMA GD Appendix M Extend utility of the RMs more elements Single concentration easier to manufacture and certify Page 5

6 REVIEW CALCULATION METHOD FOR RM VALUES Previous LBMA RMs calculated simply: Overall average and overall standard deviation (AuRM1&2, AgRM1&2) Average of averages, standard deviation of averages (AuRM3) Effect of outliers can be large Trends in reference materials produced by national laboratories: Use calculation models Look to report as accurate values as possible Look to report as appropriate an uncertainty as possible Include as much data as possible Include estimate of inhomogeneity in the uncertainty Page 6

7 CALCULATION MODELS UNDER CONSIDERATION BY LBMA RM PROJECT STEERING COMMITTEE Simple calculation (status quo) Fixed Effect Model Assumes lab measurement differ due to random effects Weighted average based on reported lab uncertainties Uncertainty calculated from reported lab uncertainties Random Effects Model Assumes lab measurements differ due random effects and biases DerSimonian Laird* (DSL) calculation method used Other methods may be used Page 7 * DerSimonian, R. and Laird, N., Meta-analysis in clinical trials, Controlled Clinical Trials, 1986, 7,

8 FIXED EFFECTS MODEL where mean i are means from individual labs, and w i are the statistic weights calculated by: Uncertainty of the mean u mean is calculated by : Page 8

9 RANDOM EFFECTS MODEL where mean i are means from individual labs, and w i are the statistic weights calculated by where u i are standard deviations from individual labs, and tau is the variability between laboratories. tau calculated by method of moments. Uncertainty of the mean u mean is calculated by : Page 9

10 AuRM3 ELEMENTS CALCULATED BY DIFFERENT METHODS Concentrations in ppm ± uncertainty (k=1) Mean of Averages Fixed Effects Random Effects (DSL method) Element Certificate Weighted Mean Weighted Mean Ag 4456 ± ± ± 23 Cu 317 ± ± ±4 Fe 21.0 ± ± ± 0.3 In 15.4 ± ± ± 0.2 Ir 6.3 ± ± ± 0.3 Observations: - Means calculated by DSL and Mean of Averages (certificate) very similar - Uncertainty by Fixed Effects unusually small for the data set - DSL uncertainty lower than certificate value (more believable) Page 10

11 AuRM3 ELEMENTS CALCULATED BY DIFFERENT METHODS Concentrations in ppm ± uncertainty (k=1) Mean of Averages Fixed Effects Random Effects (DSL method) Element Certificate Weighted Mean Weighted Mean tau Ag 4456 ± ± ± Cu 317 ± ± ±4 5.4 Fe 21.0 ± ± ± In 15.4 ± ± ± Ir 6.3 ± ± ± Observations: -tau > uncertainty inter-laboratory differences greatest source of error Page 11

12 EFFECT OF OUTLIERS ON RANDOM EFFECTS MODEL Concentrations in ppm Lab Mean, Lab Code 4465 ± 44 A 4420 ± 27 B Contributing Labs to Mean Random Effects (DSL) Mean ± 2*Uncertainty 4394 ± 19 C All labs (12) 4473 ± ± 37 D 4412± 13 E 4500 ± 18 F A,B,D,E,F,H,I,J,L,M (10) 4455 ± ± 71 G 4400 ± 18 H 4425 ± 5 I A,B,D,E,F,G,H,I,J,L,M (11) 4450 ± ± 38 J 4437 ± 39 L 4544 ± 6 M Certificate A,B,D,E,F,H,I,J,L,M (10) 4456 ± 95 Page 12

13 CALCULATE TOTAL UNCERTAINTY Include uncertainty due to mean and homogeneity Page 13

14 UNCERTAINTY DUE TO HOMOGENEITY Randomized Block Design, Spark OES 3 rows of 3 pieces = 9 pieces (from over 90 pieces) Test at 5 different depths (top, bottom, 1, 3, 5 mm depth) Z axis depths (5) X axis rows (3) Y axis columns (3) ANOVA indicated AuRM3 was sufficiently homogeneous for all elements determined Can use DSL method to calculate uncertainty in different dimension expressed as tau Page 14

15 U homo CALCULATED FROM tau BY DSL METHOD tau estimate of inter block uncertainty Axis Average Replicates Std Dev tau 2 tau 2 Average Ag Z Ag X U homo 31.9 Ag y Page 15

16 PROPOSED CALCULATION OF TOTAL UNCERTAINTY Re-calculated Concentration Values, ppm Element Mean U mean U homog U Total 2*U total Ag Cu Fe In Ir Ni Pb Pd Pt Sn Ti Zn Page 16

17 CONCLUDING REMARKS Replacement Au and Ag RMs are in progress Alternate methods of calculating mean and uncertainties are being studied Alternate methods needed: Make maximum utility of data collected Best estimates of mean or central tendency Best estimates of uncertainty In line with current chemical metrology practices Major reference material producers National Laboratories Page 17

18 ACKNOWLEDGEMENTS LBMA Ruth Crowell National Research Council of Canada Dr. Juris Meija, Institute of National Measurement Standards Page 18

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