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The mass composition of ultra-high energy cosmic rays can be studied from thedistributions of the depth of shower maximum and/or the muon shower size. Here,we study the dependence of the mean muon shower size on the depth of showermaximum in detail. Air showers induced by protons and iron nuclei weresimulated with two models of hadronic interactions already tuned with LHC data(run I-II). The generated air showers were combined to obtain various types ofmass composition of the primary beam. We investigated the shape of thefunctional dependence of the mean muon shower size on the depth of showermaximum and its dependency on the composition mixture. Fitting this dependencewe can derive the primary fractions and the muon rescaling factor with astatistical uncertainty at a level of few percent. The difference between thereconstructed primary fractions is below 20% when different models areconsidered. The difference in the muon shower size between the two models wasobserved to be around 6%.

On the Combined Analysis of Muon Shower Size and Depth of Shower Maximum