Uncertainty propagation measurement factors

Pauwels (1999) argues that the certified values of CRMs should be presented in the form of an expanded combined uncertainty according to the ISO Guide on the expression of uncertainty in measurement, so that coverage factor should always be clearly mentioned in order to allow an easy recalculation of the combined standard uncertainty. This is needed for uncertainty propagation when the CRM is used for calibration and the ISO Guide should be revised accordingly. The use of the expanded uncertainty has been pohcy in certification by NIST since 1993 (Taylor and Kuyatt 1994). 

The major components of uncertainty are combined according to the rules of propagation of uncertainty, often with the assumption of independence of effects, to give the combined uncertainty. If the measurement uncertainty is to be quoted as a confidence interval, for example, a 95% confidence interval, an appropriate coverage factor is chosen by which to multiply the combined uncertainty and thus yield the expanded uncertainty. The coverage factor should be justified, and any assumptions about degrees of freedom stated. 

Estimation of model error bars and sensitivity analyses are based rai the same principle. AU rate coefficients (or other model parameters) of a system are randomly varied within a certain range. The chemical evolution is then computed for each set of rate coefficients. For a network containing 4,000 reactions, the model is typically run 2,000 times with different sets of rate coefficients. The distribution of the rate coefficients can be either log-normal or log-uniform (see Fig. 4.5). The first choice implies that the mean value ko is a preferred value. This is usually the case for rate coefficients, which are measured with an uncertainty defined by statistical errors. The factor Fq, which defines the range of variation, can be a fixed factor for aU reactiOTis for a sensitivity analysis or specific to each reaction for an uncertainty propagation study. Use of the same Fq for all reactions, in the case of a sensitivity analysis, assures the modeller that an underestimated uncertainty factor will not bias the analysis. The results of thousands of runs are used differently to identify important reactions and to estimate model error bars. 

The uncertainty in the measurement of elution time / or elution volume of an unretained tracer is another potential source of error in the evaluation of thermodynamic quantities for the chromatographic process. It can be shown that a small relative error in the determination of r , will give rise to a commensurate relative error in both the retention factor and the related Gibbs free energy. Thus, a 5% error in leads to errors of nearly 5% in both k and AG. An analysis of error propagation showed that if the... 

Though the measurement uncertainty of each device has been checked, and care was taken to minimize measurement errors, inaccuracies of measurement cannot be ruled out. The higher peak loss factor for the resonant apparatus for example may be due to vibrational energy propagating into the dangling accelerometer cable. 

In calorimetry, often a combination of the two approaches is preferable. The calorimeter is calibrated by means of reference materials with known physical properties. In the course of the calibration, the influencing factors are varied. As a result, the scatter of the calibration values reflects the uncertainty of the calibration, provided the uncertainty of the respective physical value is small (i.e., it is at least a factor of 3 smaller). This scatter is usually quantitatively expressed by the standard deviation of the mean value. Combining this information with the scatter of repeated measurements on the sample by use of Gauss s law of error propagation renders the uncertainty of the particular experiment. If no repeated measurements can be made, the information about the probable scatter of the measurement can be inferred from historical data or the calibration measurements. 

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