Abstract
A spreadsheet method allowing rapid calculation of combined standard uncertainties is described. The model used allows explicitly for correlation effects, and requires a user to enter only the parameters, the calculation used to obtain the final result (including relevant influence factors), the individual standard uncertainties for the parameters, and estimates of correlation coefficients where necessary. The estimation of correlation coefficients in common cases is discussed, and it is shown that correlation is likely to be practically significant only when the correlated contribution to individual standard uncertainties is significantly over about 30% of the relevant standard uncertainty, leading to correlation coefficients |r| greater than 0.1. The implementation includes a more robust differentiation algorithm than previously reported for spreadsheet use, and initial preparation of the spreadsheets has been automated. The principle is illustrated with a simple example.
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Notes
Note that for many purposes it is convenient to choose c such that \( p(p',c) = p'\) and \( q(q',c) = q'\). This will normally follow where the common factor c arises from a nominally null correction, such as in the case of an assumption about which there is some uncertainty, or a calibration step with associated uncertainty.
References
ISO (1993) “Guide to the expression of uncertainty in measurement”. Geneva, Switzerland. (ISBN 92-67-10188-9)
Eurachem/CITAC Guide (2000) “Quantifying uncertainty in analytical measurement”, 2nd edition. Williams A, Ellison SLR, Roesslein M (eds). Available from the Eurachem secretariat and website (http://www.eurachem.com/) and (hard copy) LGC Ltd, London (ISBN 0-948926-15-5)
Kragten J (1994) Analyst 119:2161–2166
Haesselbarth W, Bremser W (2004) Accred Qual Assur 9:597–600
Press WH, Flannery BP, Teukolsky SA, Vettering WT (1988) Numerical recipes in C. Cambridge University Press, Cambridge NY, p 272.
Acknowledgements
This work was supported under contract with the UK Department of Trade and Industry as part of the Valid Analytical Measurement (VAM) programme. The author thanks Mr A Williams for valuable discussion.
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Ellison, S.L.R. Including correlation effects in an improved spreadsheet calculation of combined standard uncertainties. Accred Qual Assur 10, 338–343 (2005). https://doi.org/10.1007/s00769-005-0008-5
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DOI: https://doi.org/10.1007/s00769-005-0008-5