Journal of Accreditation and Quality Assurance

Journal of Accreditation and Quality Assurance

Accreditation and Quality Assurance, 2015, Springer Berlin Heidelberg. Evaluation of the expanded measurement uncertainty in the determination of the net flux of nutrients and carbon atomsthrough the liver in ruminants: Electronic Supplementary Material.

José Miguel Rodríguez-López1,2, Max Feinberg3, Denys Durand1,2, Gonzalo Cantalapiedra-Hijar1,2,AgnèsIsserty-Thomas1,2 and Isabelle Ortigues-Marty1,2

1 INRA, UMR1213 Herbivores, F-63122 Saint-Genès-Champanelle, France

2 Clermont Université, VetAgro Sup, UMR1213 Herbivores, BP 10448, F-63000, Clermont-Ferrand, France

3 INRA, 16, rue Claude Bernard, 75231 Paris cedex 05, France

* Corresponding author: e-mail: ; Tel.: +33-4-73-62-42-29; Fax: +33-4-73-62-46-39

The law of propagation of uncertainty

According to the well-known notation used in the Guide to the expression of uncertainty in measurement (GUM) [[i]], let a measurement process equation where y is an estimate of the measurandY, xiare values of input quantities and f a functional relationship. For complex relationship, the law of error propagation can be used to estimate the combined standard uncertainty of y, noted . This law is expressed in as follows:

Where is the squared estimated standard uncertainty of input quantity i and the estimated covariance of input quantities i and j. Meanwhile, are partial derivatives of function f with respect to xi. This equation can be rewritten in a more condensed way, and if variables X can be supposed as independent:

Where are called sensitivity coefficients.Thus, can simply be seen as the weighed sum of standard uncertainties of all input quantities.The major drawback of this method is that it is not always possible to compute partial derivatives. Therefore an approximate computational technique was proposed by Kragten by discretising this formula [[ii]].

If we note the predicted value of y when xi is increased of , the sensitivity coefficient for this variable is approximately equal to:

The most convenient way to select is to take the standard uncertainty and write:

Finally:

This algorithm can simply be programmed with a spreadsheet.

References

[] JCGM 100:2008, Evaluation of measurement data — Guide to the expression of uncertainty in measurement (2010) BIPM, Downloadable from

[] Kragten J. Analyst (1994) 119, 2161-2166

Tables and Figures

Table ESM.1. Example of calculation of measurement uncertainty for the net hepatic flux of non-esterified fatty acids (NEFA) in plasma

aPara-aminohippuric acid, bportal vein, chepatic vein, dmesenteric artery

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Journal of Accreditation and Quality Assurance

Table ESM.2. Example of calculation of measurement uncertainty for the net hepatic flux of lactate (Lac) in blood

aPara-aminohippuric acid, bportal vein, chepatic vein, dmesenteric artery

Figure ESM.1. Variation of measurement uncertainty as a function of the para-aminohippuric acid (pAH) concentration, noted as Ci, which represents the plasma pAH concentrations in portal or hepatic vein, mesenteric artery or in the infusate.

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