 1.

Specify the measurand and units
 2.

Describe the measurement procedure and provide the associated model equation
Measurement procedure:
Concentration of nitrate in water is measured by liquid chromatography (calibration curve).
For the final result, recovery is taken into account.
Model equation:
$$C_{{NO_{3} }} = \frac{{A  B_{0} }}{{B_{1} \cdot R}}$$
where
A,
B_{1},
B_{0} and R are measured area of the sample chromatographic peak, slope of the linear least square calibration curve, calculated blank and method recovery, respectively. Slope of the linear least square calibration curve
B_{1} and calculated blank
B_{0} are calculated from eqns:
$$B_{1} = \frac{{\sum\limits_{i = 1}^{n} {(C_{i}  \bar{C}) \cdot (A_{i}  \bar{A})} }}{{\sum\limits_{i = 1}^{n} {(C_{i}  \bar{C})^{2} } }}\quad \quad B_{0} = \bar{A}  B_{1} \cdot \bar{C}_{{}}$$
$$\bar{A} = \frac{1}{n}\sum\limits_{i = 1}^{n} {A_{i} } \quad \quad \bar{C} = \frac{1}{n}\sum\limits_{i = 1}^{n} {C_{i} }$$
$$R = \frac{{c_{observed}  c_{matrix} }}{{c_{spiked} }}$$
where
C_{i} and
A_{i} are concentration of reference solution on
ith level (
C_{1}, …,
C_{i}, …,
C_{n}) and areas of chromatographic peaks of
ith reference solution (
A_{1}, …,
A_{i}, …,
A_{n}), respectively.
 3.

Identify (all possible) sources of uncertainty
 4.

Evaluate values of each input quantity
 5.

Evaluate the standard uncertainty of each input quantity
$$\begin{aligned} \frac{{u\left( {B_{1} \times \bar{C}} \right)}}{{B_{1} \times \bar{C}}} & = \sqrt {\left( {\frac{{u(B_{1} )}}{{B_{1} }}} \right)^{2} + \left( {\frac{{u(\bar{C})}}{{\bar{C}}}} \right)^{2} } = \sqrt {\left( {\frac{831}{112837}} \right)^{2} + \left( {\frac{0.016}{3.4770}} \right)^{2} } \\ & = \sqrt {5.4237 \times 10^{  5} + 2.1175 \times 10^{  5} } = \sqrt {7.5412 \times 10^{  5} } \\ \end{aligned}$$
$$u(B_{1} \times \bar{C}) = 112837 \times 3.4770 \times \sqrt {7.5412 \times 10^{  5} } = 3407$$
$$u(B_{0} ) = \sqrt {u(\bar{A})^{2} + u(B_{1} \times \bar{C})^{2} } = \sqrt {146^{2} + 3407^{2} } = 3410$$
 6.

Calculate the value of the measurand, using the model equation
$$C_{{NO_{3} }} = \frac{{A  B_{0} }}{{B_{1} \cdot R}}\quad \quad {\text{C}}_{\text{NO3}} = 5.4\,{\text{mg}}\,{\text{L}}^{  1}$$
 7.

Calculate the combined standard uncertainty (u _{ c } ) of the result & specify units
Using:
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Mathematical solution;
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Spreadsheet Approach;
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Commercial Software
$$\begin{aligned} \frac{u\left( c \right)}{c} & = \sqrt {\left( {\frac{{u(B_{1} )}}{{B_{1} }}} \right)^{2} + \left( {\frac{u(R)}{R}} \right)^{2} + \left( {\frac{{u(A  B_{0} )}}{{A  B_{0} }}} \right)^{2} } = \sqrt {\left( {\frac{831}{112837}} \right)^{2} + \left( {\frac{0.01}{1}} \right)^{2} + \left( {\frac{5425.54}{594350 + 14967}} \right)^{2} } \\ & = \sqrt {23.35235 \times 10^{  5} } \\ \end{aligned}$$
$$u(A  B_{0} ) = \sqrt {u(A)^{2} + u(B_{0} )^{2} } = \sqrt {4220^{2} + 3410^{2} } = 5425.54$$
$$u(c) = 0.015281475 \times 5.4 = 0.082\,{\text{mg}}\,{\text{L}}^{  1}$$
u(c) = 0.082 mg L
^{−1} 8.

Calculate expanded uncertainty (U _{ c} ) & specify the coverage factor k and the units
\({\mathbf{U}}_{{\mathbf{c}}} = {\mathbf{0}}.{\mathbf{2}}\,{\text{mg}}\,{\text{L}}^{  1} \,\,({\mathbf{k}} = {\mathbf{2}})\)
 9.

Analyse the uncertainty contribution & specify the main three input quantities contributing the most to U _{ c }
 10.

Prepare your Uncertainty Budget Report