  The number of muons in extensive air showers predicted using LHC-tuned
hadronic interaction models, such as EPOS-LHC and QGSJetII-04, is smaller than
observed in showers recorded by leading cosmic ray experiments. In this paper,
we present a new method to derive muon rescaling factors by analyzing
reconstructions of simulated showers. The z-variable used (difference of
initially simulated and reconstructed total signal in detectors) is connected
to the muon signal and is roughly independent of the zenith angle but depends
on the mass of primary cosmic ray. The performance of the method is tested
using Monte Carlo shower simulations for the hybrid detector of the Pierre
Auger Observatory. Having an individual z-value from each simulated hybrid
event, the corresponding signal at 1000 m from the shower axis, and using a
parametrization of the muon fraction in simulated showers, we can calculate the
multiplicative rescaling parameters of the muon signals in the ground detector
even for an individual event. We can also study its dependence as a function of
zenith angle and the mass of primary cosmic ray. This gives a possibility not
only to test/calibrate the hadronic interaction models, but also to derive the
$\beta$-exponent, describing an increase of the number of muons as a function
of primary energy and mass of the cosmic ray. Detailed simulations show
dependence of the $\beta$-exponent on hadronic interaction properties, thus the
determination of this parameter is important for understanding the muon deficit
problem.
