Uncertainty Calculation for Complex Measurements

Abstract

Propagations of errors, or uncertainties, can be computed in different ways. The ISO Guide to the Expression of Uncertainty in Measurement (GUM) recommends an estimate based on a first-order Taylor series expansion of the functional form of the measurement equation. However, other methods may be more appropriate depending, for example, on properties of the errors in the input quantities, or nonlinearities in the measuring function. We have implemented a new method developed by C-M Wang and Hari Iyer for calculating the uncertainty of a measurement result using principles of generalized inference. Using Microsoft Excel, we developed macros for flexible uncertainty calculations based on the generalized inference method. These macros embed scripts for the open-source R statistical software system (through R DCOM Server and an Add-in for Excel). Also available are procedures for uncertainty calculations based on the common first-order Taylor series expansion method, as well as a more accurate second-order Taylor series expansion method.