Uncertainty budgeting for range calibration

The Guide to the Expression of Uncertainty in Measurement (GUM) established a general procedure to evaluate measurement uncertainty. The Guide covers only the evaluation of a single result or a set of individual results. Modern measuring instruments and procedures operate over a wide range of values. Therefore in practice a calibration procedure is needed that is valid for this range. The procedure should include an evaluation of uncertainty associated with the calibration results and for the subsequent measurements performed with the calibrated instrument. Traditionally regression analysis is used for this purpose. In this paper we will discuss some weaknesses of the regression approach and suggest an alternative. We show that for instruments with a linear response function the regression can be replaced by 2-point calibration. We introduce a limit of the deviation from linearity to address observed deviations from a linear response function of the instrument. To improve an existing instrument with a non-linear response function a combination of the instrument and a correction function can be treated as a virtual linear measuring device and a 2-point calibration can be applied. As an example we use the calibration of a pressure sensor to illustrate the procedure. The approach can be used for instruments and measurement procedures with a linear or non-linear response function.