  We elucidate the reduction of the winding number (WN) caused by the onsite
disorder in a higher WN next nearest neighbor XY model. When disorder becomes
strong enough, Majorana edge modes become critically extended, beyond which
they collapse into Anderson localized (AL) states in the bulk, resulting in a
topological Anderson insulating state (TAI). We identify a resilience threshold
$W_t$ for every pair of Majorana fermions (MFs). In response to increasing
disorder every pair of MFs collapse into AL bulk at their resilience threshold.
For very strong disorder, all Majorana fermions collapse and a topologically
trivial state is obtained. We show that the threshold values are deeply related
to the localization length of Majorana fermions, which can be efficiently
calculated by an appropriate modification of the transfer matrix method. At the
topological transition point, localization length of the zero modes diverges
and the system becomes scale invariant. The number of peaks in the localization
length as the function of disorder strength determines the number of zero modes
in the clean state before disorder is introduced. This finding elevates the
transfer matrix method to the level of a tool for determination of the
topological index of both clean and disordered systems.
