  Background channels with their expected strength and uncertainty levels are
usually known in searches of novel phenomena prior to the experiments are
conducted at their design stage. We quantitatively study the projected
sensitivities in terms of discovery potentials. These are essential for the
optimizations of the experimental specifications as well as of the
cost-effectiveness in various investment. Sensitivities in counting analysis
are derived with complete Poisson statistics and its continuous approximation,
and are compared with those using maximum likelihood analysis in which
additional measurables are included as signatures. The roles and effects due to
uncertainties in the background estimates are studied. Two expected features to
establish positive effects are verified and quantified: (i) In counting-only
experiments, the required signal strength can be derived with complete Poisson
analysis, and the continuous approximation would underestimate the results.
(ii) Incorporating continuous variables as additional constraints would reduce
the required signal strength relative to that of counting-only analysis. The
formulations are applied to the case on the experimental searches of
neutrinoless double beta decay in which both ambient and two-neutrino
background are considered.
