Measurement uncertainty interval in case of a known relationship between precision and mean

Abstract

Background: Measurement uncertainty is typically expressed in terms of a symmetric interval y±U, where y denotes the measurement result and U the expanded uncertainty. However, in the case of heteroscedasticity, symmetric uncertainty intervals can be misleading. In this paper, a different approach for the calculation of uncertainty intervals is introduced. Methods: This approach is applicable when a validation study has been conducted with samples with known concentrations. In a first step, test results are obtained at the different known concentration levels. Then, on the basis of precision estimates, a prediction range is calculated. The measurement uncertainty for a given test result can then be obtained by projecting the intersection of the test result with the limits of the prediction range back onto the axis of the known values, now interpreted as representing the measurand. Results: It will be shown how, under certain circumstances, asymmetric uncertainty intervals arise quite naturally and lead to more reliable uncertainty intervals. Conclusions:  This article establishes a conceptual framework in which measurement uncertainty can be derived from precision whenever the relationship between the latter and concentration has been characterized. This approach is applicable for different types of distributions. Closed expressions for the limits of the uncertainty interval are provided for the simple case of normally distributed test results and constant relative standard deviation.