Alternative Approaches to Uncertainty Calculations for TIMS Isotopic Measurements

Two methods of estimating uncertainty for TIMS U isotopic ratio measurements were evaluated. Although these methods represent fundamentally different approaches both are consistent with the principles outlined in the ISO "Guide to the Expression of Uncertainty in Measurements" (GUM). In the "Discrete Component" approach all of the identifiable sources of random variability associated with the mass spectrometer (gain variability, baseline variability, cup efficiency variability, Schottky noise, counting statistics) are individually assessed to estimate measurement reproducibility. The second approach is an "Integrated" method, which uses observed reproducibility of repeated identical sample measurements to confound the various components of random variability. Evaluation of the uncertainty budgets for the two methods shows that the relative importance of an uncertainty component in a measurement is highly dependent on the measurement technique and the isotopic ratio of the measured value. For example, the uncertainty of the ^{235}U/^{238}U ratio of the material analyzed in this study will generally be dominated by the uncertainty of the CRM used to determine the mass fractionation factor. The more extreme 234U/^{238}U and ^{236}U/^{238}U ratios are often dominated by other factors such as internal and external reproducibility. Although both methods are consistent with the GUM principles, there are many instrumental factors that can produce measurement variability but are not readily quantifiable (i.e., small differences in run conditions, filament geometry, sample loading, etc). Accordingly, the Discrete Component determination can accurately estimate internal reproducibility of an isotopic measurement but will not sufficiently characterize analysis-to- analysis variability that is inherent in all measurements. The Integrated approach to uncertainty evaluation has the advantage of not requiring the quantification of an extensive set of variables and also greatly simplifies the calculation of a combined standard uncertainty. This method, however, has the distinct disadvantage of requiring a statistically significant number of replicate analyses and does not allow for the determination of primary contributors to internal variability. Replicate measurements are not practical or possible for many analytical situations but it is still necessary to assess the uncertainty associated with external reproducibility. A straightforward method for estimating an external reproducibility factor for isotopic measurements is to incorporate the standard uncertainty of repeated measurements of a matrix-matched reference material or even an isotopic CRM if a matrix-matched material is unavailable.