Skip to main content
Log in

Uncertainty in repeated measurement of a small non-negative quantity: explanation and discussion of Bayesian methodology

  • Discussion Forum
  • Published:
Accreditation and Quality Assurance Aims and scope Submit manuscript

Abstract

This article considers the problem of uncertainty evaluation when there are repeated measurements of a small quantity known to be non-negative. A solution to this problem has recently been put forward by the Analytical Methods Committee of the Royal Society of Chemistry (Accred Qual Assur 13:29–32). The Bayesian statistical basis of this solution is explained and discussed. It is shown that the performance of this procedure can be poor in an important subset of measurement situations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Analytical Methods Committee, The Royal Society of Chemistry (2008) Accred Qual Assur 13:29–32

    Google Scholar 

  2. ISO (2006/1999) BS ISO 3534 (Parts 1–3) Statistics—vocabulary and symbols, International Organization for Standardization

  3. ISO (1994/1998) BS ISO 5725 (Parts 1–6) Accuracy (trueness and precision) of measurement methods and results, International Organization for Standardization

  4. Mandel J (1980) The statistical analysis of experimental data. Dover, New York

  5. Taylor JR (1997) An introduction to error analysis, 2nd edn. University Science Books, Sausalito

    Google Scholar 

  6. Coleman HW, Steele WG (1999) Experimentation and uncertainty analysis for engineers, 2nd edn. Wiley, New York

    Google Scholar 

  7. Armstrong N, Hibbert DB (2009). Chemom Intell Lab Syst 97:194–210

    Article  CAS  Google Scholar 

  8. Hibbert DB, Armstrong N (2009). Chemom Intell Lab Syst 97:211–220

    Article  CAS  Google Scholar 

  9. Marriott FHC (1990) A dictionary of statistical terms, 5th edn. International Statistical Institute, Longman, Harlow

    Google Scholar 

  10. Lindley DV (1982) Bayesian inference. In: Kotz S, Johnson NL, Read CB (eds) Encyclopedia of statistical sciences, vol 1. Wiley, New York

  11. Ehrlich C, Dybkaer C, Wöger W (2007). Accred Qual Assur 12:201–218

    Article  Google Scholar 

  12. http://physics.nist.gov

  13. Lee P M (1989) Bayesian statistics: an introduction. Oxford University Press, New York

    Google Scholar 

  14. O’Hagan A (1994) Kendall’s advanced theory of statistics, vol. 2B: Bayesian inference. Edward Arnold, London

    Google Scholar 

  15. Gelman A, Carlin JB, Stern HS, Rubin DB (1995) Bayesian data analysis. Chapman & Hall, London

    Google Scholar 

  16. Analytical Methods Committee (2008) AMCTB 26A Measurement uncertainty and confidence intervals near natural limits (re-issued September 2008). http://www.rsc.org/images/brief%2026A_tcm18-134929.pdf

  17. Hall BD (2008). Metrologia 45:L5–L8

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Robin Willink.

Additional information

Papers published in this section do not necessarily reflect the opinion of the Editors, the Editorial Board and the Publisher.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Willink, R. Uncertainty in repeated measurement of a small non-negative quantity: explanation and discussion of Bayesian methodology. Accred Qual Assur 15, 181–188 (2010). https://doi.org/10.1007/s00769-009-0595-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00769-009-0595-7

Keywords

Navigation