  The WILLI detector, built in IFIN-HH Bucharest, in collaboration with KIT
Karlsruhe, is a rotatable modular detector for measuring charge ratio for
cosmic muons with energy $<$ 1 GeV. It is under construction a mini-array for
measuring the muon charge ratio in Extensive Air Showers. The EAS simulations
have been performed with CORSIKA code. The values of the muon flux, calculated
with semi-analytical formula, and simulated with CORSIKA code, based on DPMJET
and QGSJET models for the hadronic interactions, are compared with the
experimental data determined with WILLI detector. No significant differences
between the two models and experimental data are observed. The measurements of
the muon charge ratio for different angles-of-incidence, (performed with WILLI
detector) shows an asymmetry due to the influence of magnetic field on muons
trajectory; the values are in agreement with the simulations based on DPMJET
hadronic interaction model. The simulations of muon charge ratio in EAS
performed with CORSIKA code based on three hadronic interaction models
(QGSJET2, EPOS and SYBILL) show relative small difference between models for H
and for the Fe showers; the effect is more pronounced at higher inclination of
WILLI detector. The future measurements should indicate which model is
suitable.
