Abstract
For large uncertainties, calculating the expanded uncertainty using a normal distribution for the values of the measurand can lead to negative values for the lower limit of the expanded uncertainty and unrealistic large values for the upper limit, when the relative uncertainty is constant over wide concentration range. Using the lognormal distribution overcomes these problems and is particularly important when the relative uncertainty is larger than 10%; below this value, both distributions give almost identical results. The use of the lognormal distribution can be appropriate when the model equation for the derivation of the value of the measurand consists of products of input quantities, with positive values. Most measurement results are given as a mean and a relative uncertainty, and the purpose of this paper is to show how, for a lognormal distribution, the expanded uncertainty can be derived directly from these two parameters.
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References
BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, OIML (2008) Supplement 1 to the ‘guide to the expression of uncertainty in measurement’—propagation of distributions using a Monte Carlo method. JCGM 101:2008. BIPM
Van der Veen AMH, Nieuwenkamp G (2019) Revision of ISO 19229 to support the certification of calibration gases for purity. Accred Qual Assur 24:375– 380
BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, OIML (2012) Evaluation of measurement data—the role of measurement uncertainty in conformity assessment, JCGM 106:2012. BIPM
Ellison S L R, Williams A (eds) (2012) Eurachem/CITAC Guide: quantifying uncertainty in analytical measurement, Eurachem, 3rd edition, ISBN 0 948926 15 5??. Available from the Eurachem secretariat, or from LGC Limited (London)
E. S. Keeping (1962) Introduction to Statistical Inference, University of Alberta, D. Van Nostrand Company, Inc., pp 89–90
BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, OIML (2008) Guide to the expression of uncertainty in measurement, JCGM 100:2008. JCGM 101:2008. GUM 1995 with minor corrections, Section 6.1.1
Ramsey MH, Ellison SLR (2015) Uncertainty factor: an alternative way to express measurement uncertainty in chemical measurement. Accred Qual Assur 20(2):153–155. https://doi.org/10.1007/s00769-015-1115-6
ISO/TC 69/SC 6 N 823: Measurement uncertainty in the case of large and heterogeneous variances: A new approach for the calculation of asymmetric confidence intervals. Steffen Uhlig, Petra Gowik
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Williams, A. Calculation of the expanded uncertainty for large uncertainties using the lognormal distribution. Accred Qual Assur 25, 335–338 (2020). https://doi.org/10.1007/s00769-020-01445-5
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DOI: https://doi.org/10.1007/s00769-020-01445-5