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Analytical and Bioanalytical Chemistry

, Volume 403, Issue 2, pp 537–548 | Cite as

A Bayesian approach to the evaluation of comparisons of individually value-assigned reference materials

  • Blaza Toman
  • David L. Duewer
  • Hugo Gasca Aragon
  • Franklin R. Guenther
  • George C. Rhoderick
Original Paper

Abstract

Several recent international comparison studies used a relatively novel experimental design to evaluate the measurement capabilities of participating organizations. These studies compared the values assigned by each participant to one or more qualitatively similar materials with measurements made on all of the materials by one laboratory under repeatability conditions. A statistical model was then established relating the values to the repeatability measurements; the extent of agreement between the assigned value(s) and the consensus model reflected the participants’ measurement capabilities. Since each participant used their own supplies, equipment, and methods to produce and value-assign their material(s), the agreement between the assigned value(s) and the model was a fairer reflection of their intrinsic capabilities than provided by studies that directly compared time- and material-constrained measurements on unknown samples prepared elsewhere. A new statistical procedure is presented for the analysis of such data. The procedure incorporates several novel concepts, most importantly a leave-one-out strategy for the estimation of the consensus value of the measurand, model fitting via Bayesian posterior probabilities, and posterior coverage probability calculation for the assigned 95% uncertainty intervals. The benefits of the new procedure are illustrated using data from the CCQM-K54 comparison of eight cylinders of n-hexane in methane.

Keywords

Bayesian analysis Degrees of equivalence Generalized distance regression Leave-one-out analysis Posterior coverage probability 

Notes

Acknowledgment

We thank the GAWG and its members for pioneering the comparison of multiple reference materials value-assigned by different organizations using measurements made under repeatability conditions by one organization.

Supplementary material

216_2012_5847_MOESM1_ESM.pdf (496 kb)
ESM 1 (PDF 495 kb)

References

  1. 1.
    van der Veen AMH, Brinkmann FNC, Arnautovic M et al (2007) International comparison CCQM-P41 greenhouse gases. 2. Direct comparison of primary standard gas mixtures. Metrologia 44:08003CrossRefGoogle Scholar
  2. 2.
    Wielgosz RI, Esler M, Viallon J et al (2008) International comparison CCQM-P73: nitrogen monoxide gas standards (30–70) μmol/mol. Metrologia 45:08002CrossRefGoogle Scholar
  3. 3.
    Lee J, Lee JB, Moon DM et al (2010) Final report on international key comparison CCQM-K53: oxygen in nitrogen. Metrologia 47:08005CrossRefGoogle Scholar
  4. 4.
    van der Veen AMH, Chander H, Ziel PR et al (2010) International comparison CCQM-K54: primary standard gas mixtures of hexane in methane. Metrologia 47:08019CrossRefGoogle Scholar
  5. 5.
    The BIPM key comparison database, http://kcdb.bipm.org/
  6. 6.
    JCGM 200:2008. International vocabulary of metrology—basic and general concepts and associated terms (VIM). Joint Committee for Guides in Metrology (JCGM), Sèvres, France (2008) http://www.bipm.org/en/publications/guides/vim.html
  7. 7.
    ISO. ISO 6143:2001(E) Gas analysis—comparison methods for determining and checking the composition of calibration gas mixtures. International Organization for Standardization (ISO), Geneva (2001)Google Scholar
  8. 8.
    Guenther FR, Possolo A (2011) Calibration and uncertainty assessment for certified reference gas mixtures. Anal Bioanal Chem 399:489–500CrossRefGoogle Scholar
  9. 9.
    Lehman EL (1999) Elements of large-sample theory. Springer, New YorkCrossRefGoogle Scholar
  10. 10.
    Miller RG (1981) Simultaneous statistical inference, 2nd edn. Springer, New YorkCrossRefGoogle Scholar
  11. 11.
    Fuller W (2006) Measurement error models. New York, NY: Wiley & SonsGoogle Scholar
  12. 12.
    Jeffreys H (1961) Theory of probability. New York, NY: Oxford University PressGoogle Scholar
  13. 13.
    JCGM 100:2008. Evaluation of measurement data—guide to the expression of uncertainty in measurement. Joint Committee for Guides in Metrology (JCGM), Sèvres, France (2008) http://www.bipm.org/en/publications/guides/gum.html
  14. 14.
    JCGM 101:2008. Evaluation of measurement data—supplement 1 to the “Guide to the expression of uncertainty in measurement”—propagation of distributions using a Monte Carlo method. Joint Committee for Guides in Metrology (JCGM), Sèvres, France (2008) http://www.bipm.org/en/publications/guides/gum.html
  15. 15.
    Lunn DJ, Spiegelhalter D, Thomas A, Best N (2009) The BUGS project: evolution, critique and future directions (with discussion). Stat Med 28:3049–3082CrossRefGoogle Scholar
  16. 16.
    Gelman A, Meng XL, Stern H (1996) Posterior predictive assessment of model fitness via realized discrepancies (with discussion). Stat Sin 6:733–807Google Scholar
  17. 17.
    Kacker R, Forbes A, Kessel R, Sommer K-D (2008) Bayesian posterior predictive p-value of statistical consistency in interlaboratory evaluations. Metrologia 45:512–523CrossRefGoogle Scholar

Copyright information

© Springer-Verlag (outside the USA) 2012

Authors and Affiliations

  • Blaza Toman
    • 1
  • David L. Duewer
    • 2
  • Hugo Gasca Aragon
    • 2
    • 3
  • Franklin R. Guenther
    • 2
  • George C. Rhoderick
    • 2
  1. 1.Statistical Engineering DivisionNational Institute of Science and TechnologyGaithersburgUSA
  2. 2.Analytical Chemistry DivisionNational Institute of Science and TechnologyGaithersburgUSA
  3. 3.Department of Mathematics and StatisticsUniversity of MassachusettsAmherstUSA

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