  The IceCube Neutrino Observatory, which instruments 1$\,$km$^3$ of clear ice
at the geographic South Pole, was mainly designed to detect particles with
energies in the multi-GeV to PeV range. Due to ice temperatures between
$-20^\circ$C to $-43^\circ$C and the low radioactivity of the ice, the dark
noise rates of the 5160 photomultiplier tubes forming the IceCube lattice are
of order 500 Hz, which is particularly low for 10 inch photomultipliers.
Therefore, IceCube can extend its searches to bursts of
$\mathcal{O}$(10$\,$MeV) neutrinos lasting several seconds, which are expected
to be produced by Galactic core collapse supernovae. By observing a uniform
rise in all photomultiplier rates, IceCube can provide a particularly high
statistical precision for the neutrino rate from supernovae in the inner part
of our Galaxy ($<$ 20 kpc). In this paper, the tools and the method to study
potential obscured or failed core collapse supernovae in our Galaxy are
presented. The analysis will be based on 3911 days of IceCube data taken
between April 17, 2008 and December 31, 2018.
