  Direct sampling of neutral interstellar (NIS) atoms by the Interstellar
Boundary Explorer (IBEX) can potentially provide a complementary method for
studying element abundances in the Local Interstellar Cloud and processes in
the heliosphere interface.}{We set the stage for abundance-aimed in-depth
analysis of measurements of NIS He, Ne, and O by IBEX and determine systematic
differences between abundances derived from various calculation methods and
their uncertainties.}{Using a model of ionization rates of the NIS species in
the heliosphere, based on independent measurements of the solar wind and solar
EUV radiation, we develop a time-dependent method of calculating the survival
probabilities of NIS atoms from the termination shock (TS) of the solar wind to
IBEX. With them, we calculate densities of these species along the Earth's
orbit and simulate the fluxes of NIS species as observed by IBEX. We study
pairwise ratios of survival probabilities, densities and fluxes of NIS species
at IBEX to calculate correction factors for inferring the abundances at
TS.}{The analytic method to calculate the survival probabilities gives
acceptable results only for He and Ne during low solar activity. For the
remaining portions of the solar cycle, and at all times for O, a fully time
dependent model should be used. Electron impact ionization is surprisingly
important for NIS O. Interpreting the IBEX observations using the time
dependent model yields the LIC Ne/O abundance of $0.16\pm40%$. The uncertainty
is mostly due to uncertainties in the ionization rates and in the NIS gas flow
vector.}{The Ne/He, O/He and Ne/O ratios for survival probabilities, local
densities, and fluxes scaled to TS systematically differ and thus an analysis
based only on survival probabilities or densities is not recommended, except
the Ne/O abundance for observations at low solar activity.
