Examples of S1 coverage intervals with very good and very bad long-run success rate

The paper illustrates, by means of selected examples, the merits and the limits of the method for computing coverage intervals described in the Supplement 1 to the GUM. The assessment of coverage intervals is done by evaluating their long-run success rate. Three pairs of examples are presented, relative to three different ways of generating incomplete knowledge about quantities: toss of dice, presence of additive noise, quantization. In all the pairs of examples, the first one results in a coverage interval with a long-run success rate equal to the coverage probability (set to 95%); the second one, instead, yields an interval with a success rate near to zero. The paper shows that the propagation mechanism of the Supplement 1, while working well in certain special cases, yields unacceptable results in others, and that the problematic issues cannot be neglected. The conclusion is that, if a Bayesian approach to uncertainty evaluation is adopted, the propagation is a particularly delicate issue.