Calculating Measurement Uncertainties for Mass Spectrometry Data

A complete and transparent characterization of measurement uncertainty is fundamentally important to the interpretation of analytical results. We have observed that the calculation and reporting of uncertainty estimates for isotopic measurement from a variety of analytical facilities are inconsistent, making it difficult to compare and evaluate data. Therefore, we recommend an approach to uncertainty estimation that has been adopted by both US national metrology facilities and is becoming widely accepted within the analytical community. This approach is outlined in the ISO "Guide to the Expression of Uncertainty in Measurement" (GUM). The GUM approach to uncertainty estimation includes four major steps: 1) Specify the measurand; 2) Identify uncertainty sources; 3) Quantify components by determining the standard uncertainty (u) for each component; and 4) Calculate combined standard uncertainty (u_c) by using established propagation laws to combine the various components. To obtain a desired confidence level, the combined standard uncertainty is multiplied by a coverage factor (k) to yield an expanded uncertainty (U). To be consistent with the GUM principles, it is also necessary create an uncertainty budget, which is a listing of all the components comprising the uncertainty and their relative contribution to the combined standard uncertainty. In mass spectrometry, Step 1 is normally the determination of an isotopic ratio for a particular element. Step 2 requires the identification of the many potential sources of measurement variability and bias including: gain, baseline, cup efficiency, Schottky noise, counting statistics, CRM uncertainties, yield calibrations, linearity calibrations, run conditions, and filament geometry. Then an equation expressing the relationship of all of the components to the measurement value must be written. To complete Step 3, these potential sources of uncertainty must be characterized (Type A or Type B) and quantified. This information is often readily available (e.g., CRM Certificate Values) but for some variables it may not be possible or practical to quantify uncertainty (e.g., filament geometry effects). Therefore, to complete step 4 and calculate a combined standard uncertainty, an approach that confounds many of the potential sources of measurement uncertainty may be required. The uncertainty calculated using the GUM approach should be reported in an uncertainty budget, which is generated using the equation created in Step 2 and evaluating each uncertainty component by either an analytical method or a numerical approach.