Analysis of natural gas by gas chromatography Reduction of correlated uncertainties by normalisation
(2004)
The results of gas chromatographic analysis of natural gas mixtures reveal strong correlations (Pearson correlation coefficient of >0.96) between the uncertainty of each component and variations in the ambient pressure. Although correction for ambient pressure variations can reduce this variability, normalisation of the results of each analysis using the assumption that the sum of all component amount fractions is unity provides significantly greater reductions in the uncertainty of each measured component. We show that the uncertainty in normalised components can be estimated approximately using the correlation coefficient as a measure of the correlation present in the measurements, or exactly using a full calculation of the variance/covariance (V/C) structure of the data.
With measurement uncertainty estimation accounting for all relevant uncertainty contributions, the results of measurements using the same procedure on different objects or samples may no longer be considered as being independent, and correlations have to be taken into account. For this purpose, a simple approximation for the estimation of covariances is derived and applied to the estimation of uncertainty for some basic combinations of two measurement results. This covariance estimate is also applied to the estimation of uncertainty for the mean value of the results of replicate measurements on the same object or sample.
In the second part of this two-part series on the state-of-the-art comparability of corrected emission spectra, we have extended this assessment to the broader community of fluorescence spectroscopists by involving 12 field laboratories that were randomly selected on the basis of their fluorescence measuring equipment. These laboratories performed a reference material (RM)-based fluorometer calibration with commercially available spectral fluorescence standards following a standard operating procedure that involved routine measurement conditions and the data evaluation software LINKCORR developed and provided by the Federal Institute for Materials Research and Testing (BAM). This instrument-specific emission correction curve was subsequently used for the determination of the corrected emission spectra of three test dyes, X, QS, and Y, revealing an average accuracy of 6.8% for the corrected emission spectra. This compares well with the relative standard uncertainties of 4.2% for physical standard-based spectral corrections demonstrated in the first part of this study (previous paper in this issue) involving an international group of four expert laboratories. The excellent comparability of the measurements of the field laboratories also demonstrates the effectiveness of RM-based correction procedures.
The development of fluorescence applications in the life and material sciences has proceeded largely without sufficient concern for the measurement uncertainties related to the characterization of fluorescence instruments. In this first part of a two-part series on the state-of-the-art comparability of corrected emission spectra, four National Metrology Institutes active in high-precision steady-state fluorometry performed a first comparison of fluorescence measurement capabilities by evaluating physical transfer standard (PTS)-based and reference material (RM)-based calibration methods. To identify achievable comparability and sources of error in instrument calibration, the emission spectra of three test dyes in the wavelength region from 300 to 770 nm were corrected and compared using both calibration methods. The results, obtained for typical spectrofluorometric (0°/90° transmitting) and colorimetric (45°/0° front-face) measurement geometries, demonstrated a comparability of corrected emission spectra within a relative standard uncertainty of 4.2% for PTS- and 2.4% for RM-based spectral correction when measurements and calibrations were performed under identical conditions. Moreover, the emission spectra of RMs F001 to F005, certified by BAM, Federal Institute for Materials Research and Testing, were confirmed. These RMs were subsequently used for the assessment of the comparability of RM-based corrected emission spectra of field laboratories using common commercial spectrofluorometers and routine measurement conditions in part 2 of this series (subsequent paper in this issue).
The measurement uncertainty is useful to estimate the confidence of analytical results. Nowadays, a result without the uncertainty statement cannot be considered reliable, but the scientific literature still lacks examples of the estimate of the measurement uncertainty. This paper presents a practical and reliable description of the measurement uncertainty estimation of the analytical determination of ethyl carbamate in cachaça by GC-IDMS. The isotope dilution technique (ID) associated with GC-MS was used to improve the accuracy. The uncertainty estimated corresponds to 10% of the mass fraction of ethyl carbamate (115 ± 11) ng/g, which is in agreement with ppb level.