  In counting experiments, one can set an upper limit on the rate of a Poisson
process based on a count of the number of events observed due to the process.
In some experiments, one makes several counts of the number of events, using
different instruments, different event detection algorithms, or observations
over multiple time intervals. We demonstrate how to generalize the classical
frequentist upper limit calculation to the case where multiple counts of events
are made over one or more time intervals using several (not necessarily
independent) procedures. We show how different choices of the rank ordering of
possible outcomes in the space of counts correspond to applying different
levels of significance to the various measurements. We propose an ordering that
is matched to the sensitivity of the different measurement procedures and show
that in typical cases it gives stronger upper limits than other choices. As an
example, we show how this method can be applied to searches for
gravitational-wave bursts, where multiple burst-detection algorithms analyse
the same data set, and demonstrate how a single combined upper limit can be set
on the gravitational-wave burst rate.
