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We assess the ability of the Holland model to accurately predict phonon-phonon relaxation times from bulk thermal conductivity values. First, lattice dynamics calculations are used to obtain phonon-phonon relaxation times and thermal conductivities for temperatures ranging from 10 K to 1000 K for Stillinger-Weber silicon. The Holland model is then fitted to these thermal conductivities and used to predict relaxation times, which are compared to the relaxation times obtained by lattice dynamics calculations. We find that fitting the Holland model to both total and mode-dependent thermal conductivities does not result in accurate mode-dependent phonon-phonon relaxation times. Introduction of Umklapp scattering for longitudinal modes resulted in improved prediction of mode-dependent relative contributions to thermal conductivity, especially at high temperatures. However, assumptions made by Holland regarding the frequency-dependence of phonon scattering mechanisms are found to be inconsistent with lattice dynamics data. Instead, we introduce a simple method based on using cumulative thermal conductivity functions to obtain better predictions of the frequency-dependence of relaxation times.