We present a procedure for calculating an upper limit on the number of signal
events which incorporates the Poisson uncertainty in the background, estimated
from control regions of one or two dimensions. For small number of signal
events, the upper limit obtained is more stringent than that extracted without
including the Poisson uncertainty. This trend continues until the number of
background events is comparable with the signal. When the number of background
events is comparable or larger than the signal, the upper limit obtained is
less stringent than that extracted without including the Poisson uncertainty.
It is therefore important to incorporate the Poisson uncertainty into the upper
limit; otherwise the upper limit obtained could be too stringent.Comment: 14 pages, 4 figure
