  The origin and nature of the cosmic rays is still uncertain. However, a big
progress has been achieved in recent years due to the good quality data
provided by current and recent cosmic-rays observatories. The cosmic ray flux
decreases very fast with energy in such a way that for energies $\gtrsim
10^{15}$ eV, the study of these very energetic particles is performed by using
ground based detectors. These detectors are able to detect the atmospheric air
showers generated by the cosmic rays as a consequence of their interactions
with the molecules of the Earth's atmosphere. One of the most important
observables that can help to understand the origin of the cosmic rays is the
composition profile as a function of primary energy. Since the primary particle
cannot be observed directly, its chemical composition has to be inferred from
parameters of the showers that are very sensitive to the primary mass. The two
parameters more sensitive to the composition of the primary are the atmospheric
depth of the shower maximum and the muon content of the showers. Past and
current cosmic-rays observatories have been using muon counters with the main
purpose of measuring the muon content of the showers. Motivated by this fact,
in this work we study in detail the estimation of the number of muons that hit
a muon counter, which is limited by the number of segments of the counters and
by the pile-up effect. We consider as study cases muon counters with
segmentation corresponding to the underground muon detectors of the Pierre
Auger Observatory that are currently taking data, and the one corresponding to
the muon counters of the AGASA Observatory, which stopped taking data in 2004.
