Generalized expressions of second and third order for the evaluation of standard measurement uncertainty

The Guide to the Expression of Uncertainty in Measurement (GUM) requires the use of a first-order Taylor series expansion for propagating uncertainties. However, when the measurement function is strongly non-linear the use of this linear approximation may be inadequate and therefore higher order terms from the Taylor series cannot be neglected. The present paper aims to derive generalized expressions of second and third order for the evaluation of the estimate of a measurand and its associated standard uncertainty. A case study is given to illustrate an application of the proposed methods and the results obtained with the GUM method are compared to the corresponding ones when applying the method proposed in GUM Supplement 1.

► We derive generalized expressions of second and third order for both the estimate and standard uncertainty of a measurand.
► A comparison of the proposed method with the GUM and GUM Supplement 1 methods is outlined.
► We conclude that these expressions can be useful for evaluating the measurement uncertainty in non-linear models.