Both silver chalcogenides (Ag2S, Ag2Se, and Ag2Te) and silver halides (AgCl, AgBr, and AgI) are known to be fast-ion solids in which the silver ions can diffuse quickly in a sublattice formed by the other ions. To clarify whether mixtures of these materials (such as Ag3SeI) possess comparable properties and whether a systematic dependence on the cation-to-anion ratio can be observed, some of these mixtures were studied by quasielastic neutron scattering both in the solid and the liquid phases. To identify the diffusion mechanisms and constants, a new data-analysis method based on a two-dimensional maximum-likelihood fit is proposed. This method has the potential to give more reliable information on the diffusion mechanism than the traditional Bayesian method.