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A new model is developed for the analysis of muon spin relaxation (μSR) measurements of muonium (Mu) reaction rates with other chemical species. The kinetics component of the model is specifically developed for addition reactions but can be extended to direct reactions. The polarization component of the model assumes that the adduct formed possesses a single, effective spin precession frequency. The complete model is solved to obtain an analytic expression for the μSR signal as a function of time. Both a time-ordered sequence method and a Boltzmann spin equation method give equivalent solutions. These solutions are analyzed under various kinetic conditions. It is concluded that the coefficient controlling the decay of the μSR signal is closely related to the adduct formation rate constant, i.e., the high pressure limit of the apparent bimolecular addition rate constant. In the most favorable case, the decay constant gives the adduct formation rate constant directly at all pressures of buffer gas. [ABSTRACT FROM AUTHOR]