Accred. Qual. Assur., Springer, Berlin and Heidelberg, 2013

Target measurement uncertainty as a tool for validation of uncertainties estimated by different approaches. Determination of total hardness in drinking and natural waters.

Sandra Calisto, Maria Esquível,Maria Trancoso

Electronic Supplementary Material

Equations used for estimation of measurement uncertainty

Calcium quality control standard (QCS) mass concentration, , with = 0.99 g L-1 was prepared as described to, using a different batch of reagent. The values were estimated by:

(A.1)

being the mass of standard reagent used to prepare QCS, P the purity of standard reagent,the volume QCS measured with a pipette, the volume of the flask used to prepare QCS and the volume of flask volume used for QCS dilution.The was estimated by Eq. A.2:

(A.2)

The, and values were obtained by the Eq. (A.3) accounting also the uncertainty associated with the repeatability, . This component was estimated by ¼ of the volume tolerance given by manufacture [18],and assuming a rectangular distribution.

(A.3)

The value was estimated using Eq. (A.4) considering the repeatability uncertainty, estimated from 1g standard weightings (n=5).

(A.4)

In Table A.1 the uncertainty budget for = 9.9 mg L-1 are shown as an example.

Table A.1 Uncertainty budget for = 9.9 mg L-1
Quantity / Value / / Units / / Degrees of freedom / Type of evaluation / Distribution
P / 0.9900 / 0.0058 / g/g / 0.0099 / ∞ / B / rectangular
/ 1000 / 0.155 / mg / 10.0000 / 95 / Contribution bellow*
/ 1000 / 0.00065 / L / -9.9 / ∞ / B / rectangular
/ 0.5 / 0.0042 / mL / 19.8000 / ∞ / B / rectangular
/ 50 / 0.047 / mL / -0.1980 / ∞ / B / rectangular
/ 9.90 / 0.10 a) / mg L-1 / ∞
(k = 2, p95 %) / 0.20 / mg L-1
*Mass contribution / / Units / / Degrees of freedom / Type of evaluation / Distribution
mcal / 0.139 / mg / - / 95 / A / normal
mrel / 0.041 / mg / - / ∞ / B / rectangular
mrep / 0.055 / mg / - / 4 / A / normal
/ 0.155 / mg / 95
-QCS mass concentration (Eq. A.1); QCS – quality control standard; - sensitivity coefficient given by ; - mass of CaCO3 standard reagent used to prepare QCS (mg); P - purity of CaCO3 standard reagent (g/g); - volume of flask volume used for QCS dilution; - QCS volume measured with a pipette; - volume of the flask used to prepare QCS;mcal - uncertainty source duetobalance calibration estimated from the certificate of calibration; mrel - uncertainty source from digital resolution; mrep- uncertainty source duetoweighing repeatability; - expanded uncertainty of ; - combined standard uncertainty of (Eq. A.4); - standard uncertainty of ; a) estimated from Eq. A.2.

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