Comparison of Measured Quantity Value Estimators in Nonlinear Models

The criterion for choosing the method to estimate measurand values when repeated measurements are performed is not clearly addressed in the Guide to the Expression of Uncertainty in Measurement (GUM). In the authors’ opinion, this is due to the lack of a clear and univocal distinction between the concepts of definitional and acquisition uncertainty. In fact, definitional uncertainty sources derive from the very definition of the input quantities of the measurement model, and as such, they unavoidably become part of the quantity to be measured. On the contrary, acquisition uncertainty contributions affect the measurement of the input quantities, and therefore, they should properly be estimated and, if possible, reduced. While a proper distinction between definitional and acquisition uncertainties is not significant when the measurement model is linear, this may become critical when the measured quantity value is the output of a nonlinear function. Accordingly, in this paper, the two methods recommended in the GUM to estimate the values of a measurand resulting from a function of a single input quantity are compared thus leading to some criteria for selecting the preferable method on the basis of the amount of definitional and acquisition uncertainty contributions.