Hypothesis test on the ratio between two measurement uncertainties

In a measurement context often it is fundamental to verify if two independent measurement processes give origin to the same uncertainty. The comparison between these two uncertainties is important, for instance when we use two or more different instruments. We apply this method to the uncertainty of a digital oscilloscope measuring rise/fall time of a signal. We apply this test to verify this property if it is requested by other important hypothesis tests like that about the difference between the measurand estimators. This technique is also the base to the ANOVA (ANalysis Of VAriance) procedure. Such statistical tools are widely adopted in the measurement since to draw conclusions from experimental results, see for example [1-3].