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Zusammenfassung
If the value of a derived measurement standard is assigned by comparison with a reference standard of the same quantity, the uncertainty is increased by the additional uncertainty on the difference measurement. This basic fact has lead to the general belief that the uncertainty of derived standards is always larger than that of the reference standards. However, if the value of a derived standard is assigned by comparison with several independent reference standards using an appropriate average, the increase of uncertainty due to the uncertainty on difference measurement may be counterbalanced by the the well-known decrease of uncertainty through averaging. The gain of accuracy made possible by this mechanism is restricted to second-generation standards. Further gain through iteration is prevented by correlation between standards derived from the same set of reference standards. As a consequence, the concept of metrological hierarchy levels, relating to traceability chains, becomes questionable for traceability networks.
Uncertainty propagation via preparation, calibration and comparison steps in traceability networks
(1999)
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.
The 'uncertainty matrix', i.e. the variance/covariance matrix associated with a set of values obtained by measurement of multiple measurands, is discussed as the multivariate analogue of the standard uncertainty (or rather the variance) of a value obtained for a single measurand. The main topics are the characterization and comparison of uncertainty matrices with respect to the level of uncertainty of derived quantities and the level of correlation effects on the uncertainty of derived quantities. Examples include a comprehensive application study on the normalization of natural gas composition data. Supplementary technical material such as basic properties of uncertainty matrices and mathematical proofs are included in an appendix.