  The MAJORANA DEMONSTRATOR is an experiment constructed to search for
neutrinoless double-beta decays in germanium-76 and to demonstrate the
feasibility to deploy a ton-scale experiment in a phased and modular fashion.
It consists of two modular arrays of natural and $^{76}\textrm{Ge}$-enriched
germanium detectors totaling 44.1 kg (29.7 kg enriched detectors), located at
the 4850' level of the Sanford Underground Research Facility in Lead, South
Dakota, USA. Data taken with this setup since summer 2015 at different
construction stages of the experiment show a clear reduction of the observed
background index around the ROI for $0\nu\beta\beta$-decay search due to
improvements in shielding. We discuss the statistical approaches to search for
a $0\nu\beta\beta$-signal and derive the physics sensitivity for an expected
exposure of $10\,\textrm{kg}{\cdot}\textrm{y}$ from enriched detectors using a
profile likelihood based hypothesis test in combination with toy Monte Carlo
data.
