  We define some appropriate statistical quantities that indicate the physical
significance (reliability) of confidence intervals in the framework of both
Frequentist and Bayesian statistical theories. We consider the expectation
value of the upper limit in the absence of a signal (that we propose to call
"exclusion potential", instead of "sensitivity" as done by Feldman and Cousins)
and its standard deviation, we define the "Pull" of a null result, expressing
the reliability of an experimental upper limit, and the "upper and lower
detection functions", that give information on the possible outcome of an
experiment if there is a signal. We also give a new appropriate definition of
"sensitivity", that quantifies the capability of an experiment to reveal the
signal that is searched for at the given confidence level.
