  The atmospheric neutrino passing fraction, or self-veto, is defined as the
probability for an atmospheric neutrino not to be accompanied by a detectable
muon from the same cosmic-ray air shower. Building upon previous work, we
propose a redefinition of the passing fractions by unifying the treatment for
muon and electron neutrinos. Several approximations have also been removed.
This enables performing detailed estimations of the uncertainties in the
passing fractions from several inputs: muon losses, cosmic-ray spectrum,
hadronic-interaction models and atmosphere-density profiles. We also study the
passing fractions under variations of the detector configuration: depth,
surrounding medium and muon veto trigger probability. The calculation exhibits
excellent agreement with passing fractions obtained from Monte Carlo
simulations. Finally, we provide a general software framework to implement this
veto technique for all large-scale neutrino observatories.
