A Monte-Carlo method for the generation of muon decay histograms in the presence of charge-exchange processes between different muonium states is presented. The simulation is based on the ROOT toolkit developed at CERN. Histograms are saved in root file format and can be directly analysed using the musrfit framework recently developed at PSI [1]. The simulation is tested by comparing with the measured temperature dependence of the diamagnetic asymmetry in Si in the Mu_BC⁰ ionization regime.