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Half-Heusler alloys have been the focus of recent experimental research as emerging thermoelectric materials. Particular attention has been focused on the MNiSn (M=Ti, Zr, and Hf) alloys with substitutions made to reduce the lattice thermal conductivity and enhance the electrical transport properties. The effect of these substitutions on the relaxation time of phonon scattering in the material, and the impact on the lattice thermal conductivity, was investigated with a focus on modeling the experimental data. A modified Callaway model was used to describe experimental data, which were then compared to theoretical results predicted using phonon scattering by mass fluctuation and strain field models. The correlation between the coefficients obtained with experimental fits and theoretical models shows a predictable and systematic relationship between alloy composition and the thermal conductivity. In addition, the role of the normal (N) phonon-phonon scattering process is investigated following a recent theoretical study that indicated that the effect of N-process was underestimated in original Callaway's model. A comparison of the lattice thermal conductivity behavior using the phonon relaxation times in the original Callaway's model and the newly suggested theoretical model by Allen for the normal process is presented and discussed. [ABSTRACT FROM AUTHOR]