Including Covariances in Calibration to Obtain Better Measurement Uncertainty Estimates

Decisions are often based on the results of quantitative analysis. To gain confidence in these results, some indication of their quality is needed. Measurement uncertainty, as proposed by the International Organization for Standardization (ISO), is a way to express this quality. Most measurement techniques compare references and therefore need to be calibrated. Usually least squares methods ignoring uncertainties associated with the calibration references are applied. In this article we show how the measurement uncertainty can be computed in compliance with the ISO proposal, taking into account the covariances of the calibration references. Two new fitting methods, XiP–fit and P–fit, are devised and compared to other fitting methods. For our examples the P–fit method outperforms the other methods in terms of parameter recovery. Additionally, we introduce a solver which is well suited for the class of problems arising from calibration and measurement uncertainty estimation.