  Majorana bound states (MBS) are well-established in the clean limit in chains
of ferromagnetically aligned impurities deposited on conventional
superconductors with finite spin-orbit coupling. Here we show that these MBS
are very robust against disorder. By performing self-consistent calculations we
find that the MBS are protected as long as the surrounding superconductor show
no large signs of inhomogeneity. We find that longer chains offer more
stability against disorder for the MBS, albeit the minigap decreases, as do
increasing strengths of spin-orbit coupling and superconductivity.
