  A typical experiment in high energy physics is considered. The result of the
experiment is assumed to be a histogram consisting of bins or channels with
numbers of corresponding registered events. The expected background and
expected signal shape or acceptance are measured in separate auxiliary
experiments, or calculated by the Monte Carlo method with finite sample size,
and hence with finite precision. An especially complex situation occurs when
the expected background in some of the channels happens to be zero due to
either a fluctuation of the auxiliary measurement (or simulation) or because it
is truly zero. Different statistical methods give different confidence
intervals for the full signal rate and different significances of the
signal+background hypothesis versus the pure background hypothesis. Detailed
analysis and numerical tests are presented.
