Comparison of ISO-GUM, draft GUM Supplement 1 and Bayesian statistics using simple linear calibration

We compare three approaches for quantifying uncertainty through a measurement equation: the International Organization for Standardization (ISO) Guide to the Expression of Uncertainty in Measurement (GUM), draft GUM Supplement 1 and Bayesian statistics. For illustration, we use a measurement equation for simple linear calibration that includes both Type A and Type B input variables. We consider three scenarios: (i) the measurement equation is linear with one Type B input variable having a normal distribution, (ii) the measurement equation is non-linear with two Type B input variables each having a normal distribution and (iii) the measurement equation is non-linear with two Type B input variables each having a rectangular distribution. We consider both small and large uncertainties for the Type B input variables. We use each of the three approaches to quantify the uncertainty in measurement for each of the three scenarios. Then we discuss the merits and limitations of each approach.