Combined Standard Uncertainty of the measurement#
The combination of all the standard uncertainties associated with the input quantities in the measurement model (VIM (BIPM)). Also called overall uncertainty.
The combined uncertainty, or overall uncertainty, is calculated using the law of propagation of the uncertainties (considering that the standard uncertainties are not correlated) according to the Guide to the Expression of Uncertainty in Measurement .
Formula:
\(u\left(\chi _{\mathrm{precision}}\right)\) : Uncertainty of the measurement method associated to the reproducibility
\(u\left(\chi _{\mathrm{calibration}}\right)\) : Uncertainty of the calibration RGM
\(u\left(\chi _{\mathrm{instrument}}\right)\) : Uncertainty of the analytical system
\(u\left(\chi _{\mathrm{sampling}}\right)\) : Uncertainty of the sampling system
Uncertainty linked to the reproducibility of the measurement method (Precision)#
The precision is a measure for the closeness of the agreement between measured values obtained by replicate measurements on the same or similar objects under specified conditions (VIM (BIPM)). This is expressed as standard uncertainty reflecting the variability of the measurement system due to random errors.
Formula:
\(\chi _{\mathrm{sample}}\) : Amount fraction of a substance in a sample
\(\sigma^{\mathrm{rel}}_{\mathrm{series}}\) : relative standard deviation of calibrations
\(\mathrm{LOD}\) : Detection Limit
Uncertainty of the Calibration#
Standard uncertainty due to the calibration. Behaviour not defined for calculation using the FID formula.
Formula:
\(A_{\mathrm{sample}}\) : Peak area of sample measurement
\(A_{\mathrm{calib}}\) : Peak area of calibration gas measurement
\(A_{\mathrm{blank}}\) : Possible blank area value determined in zero gas measurements
\(V_{\mathrm{calib}}\) : Volume of calibration gas samples
\(V_{\mathrm{sample}}\) : Volume of measured samples
\(u_{\mathrm{calib}}\) : Certified uncertainty of the RGM amount fraction
\(\chi _{\mathrm{sample}}\) : Amount fraction of a substance in a sample
\(\chi _{\mathrm{calib}}\) : Certified amount fraction of calibration gas
Uncertainty of the Instrument#
The overall uncertainty of the instrument is the result of combining the standard uncertainties of the peak integration, sample volume, further instrumental problems (e.g. sampling line artefacts) and the uncertainty due to the lack of linearity.
Formula:
\(u\left(\chi _{\mathrm{peak\ integration}}\right)\) : Uncertainty of the Peak Integration
\(u\left(\chi _{\mathrm{volume}}\right)\) : Uncertainty of the Volume
\(u\left(\chi _{\mathrm{further\ instrumental\ problems}}\right)\) : Uncertainty of the Further Instrumental Problems
\(u\left(\chi _{\mathrm{linearity}}\right)\) : Uncertainty of the Linearity
Uncertainty of the Peak Integration#
The standard uncertainty due to peak integration.
Formula:
\(f_{\mathrm{calib}}\) : Calibration Factor
\(V_{\mathrm{sample}}\) : Volume of measured samples
\(\frac{u\left(A_{\mathrm{int,}sample}\right)}{A_{\mathrm{sample}}}\) : Uncertainty from peak integration in the measurement
\(A_{\mathrm{sample}}\) : Peak area of sample measurement
\(V_{\mathrm{calib}}\) : Volume of calibration gas samples
\(\chi _{\mathrm{calib}}\) : Certified amount fraction of calibration gas
\(A_{\mathrm{calib}}\) : Peak area of calibration gas measurement
\(\frac{u\left(A_{\mathrm{int,}calib}\right)}{A_{\mathrm{calib}}}\) : Uncertainty from peak integration in the calibration
Uncertainty of the Volume#
The standard uncertainty due to the difference between sampling and calibration volumes.
Formula:
\(\chi _{\mathrm{sample}}\) : Amount fraction of a substance in a sample
\(u\left(V_{\mathrm{sample}}\right)\) : Uncertainty of the measured sample volume
\(u\left(V_{\mathrm{calib}}\right)\) : Uncertainty of the calibration volume
\(V_{\mathrm{sample}}\) : Volume of measured samples
\(V_{\mathrm{calib}}\) : Volume of calibration gas samples
Uncertainty of the Further Instrumental Problems#
Standard uncertainty due to specific instrumental problems.
Formula:
\(\chi _{\mathrm{sample}}\) : Amount fraction of a substance in a sample
\(u_{\mathrm{instrument}}\) : Systematic Instrument Error
Uncertainty of the Linearity#
Standard uncertainty due to lack of linearity of the measurement system.
Formula:
\(u_{\mathrm{linearity}}\) : Uncertainty from non-linearity
Uncertainty of the sampling method#
The standard uncertainty due to application of off-line sampling techniques depends on the technique used. Contributions to the uncertainty common to all off-line techniques (cleaning of the samplers, storage, adsorption effects, etc.) should be evaluated case-by-case and per individual component. If not available in literature, a proper validation of the sorbent tubes is recommended prior to their use in the field to establish the efficiency of adsorption/desorption and the safe sampling volume at different composition levels and atmospheric conditions.
Formula:
\(u_{\mathrm{sampling}}\) : Uncertainty from sampling volume accuracy
Uncertainty of the Blank#
The uncertainty due to the deviation of blank samples from the mean blank values.
Formula:
\(\sigma _{\mathrm{blank}}\) : standard deviation of the amount fraction of a serie of blank runs
Expanded Uncertainty#
The combined uncertainty is the product of the combined standard uncertainty of the measurement by a number greater than 1 (the coverage factor k).
Formula:
\(u\left(\chi _{\mathrm{sample}}\right)\) : Combined Standard Uncertainty