  Recent results obtained from leading cosmic ray experiments indicate that
simulations using LHC-tuned hadronic interaction models underestimate the
number of muons in extensive air showers compared to experimental data. This is
the so-called muon deficit problem. Determination of the muon component in the
air shower is crucial for inferring the mass of the primary particle, which is
a key ingredient in the efforts to pinpoint the sources of ultra-high energy
cosmic rays.In this paper, we present a new method to derive the muon signal in
detectors, which uses the difference between the total reconstructed (data) and
simulated signals is roughly independent of the zenith angle, but depends on
the mass of the primary cosmic ray. Such a method offers an opportunity not
only to test/calibrate the hadronic interaction models, but also to derive the
$\beta$ exponent, which describes an increase of the number of muons in a
shower as a function of the energy and mass of the primary cosmic ray. Detailed
simulations show a dependence of the $\beta$ exponent on hadronic interaction
properties, thus the determination of this parameter is important for
understanding the muon deficit problem. We validate the method by using Monte
Carlo simulations for the EPOS-LHC and QGSJetII-04 hadronic interaction models,
and showing that this method allows us to recover the ratio of the muon signal
between EPOS-LHC and QGSJetII-04 and the average $\beta$ exponent for the
studied system, within less than a few percent. This is a consequence of the
good recovery of the muon signal for each primary included in the analysis.
