  The origin and nature of ultra high energy cosmic rays remains being a
mystery. However, great progress has been made in recent years due to the
observations performed by the Pierre Auger Observatory and Telescope Array. In
particular, it is believed that the composition information of the cosmic rays
as a function of the energy can play a fundamental role for the understanding
of their origin. The best indicators for primary mass composition are the muon
content of extensive air shower and the atmospheric depth of the shower
maximum. In this work we consider a maximum likelihood method to perform mass
composition analyses based on the number of muons measured by underground muon
detectors. The analyses are based on numerical simulations of the showers. The
effects introduced by the detectors and the methods used to reconstruct the
experimental data are also taken into account through a dedicated simulation
that uses as input the information of the simulated showers. In order to
illustrate the use of the method, we consider AMIGA (Auger Muons and Infill for
the Ground Array), the low energy extension of the Pierre Auger Observatory
that directly measures the muonic content of extensive air showers. We also
study in detail the impact of the use of different high energy hadronic
interaction models in the composition analyses performed. It is found that
differences of a few percent between the predicted number of muons have a
significant impact on composition determination.
