  We study the influence of inelastic rare-earth impurity scattering on
electron-phonon mediated superconductivity and mass renormalization in
(La$_{1-x}$Pr$_{x}$)Os$_{4}$Sb$_{12}$ compounds. Solving the strong coupling
Eliashberg equations we find that the dominant quadrupolar component of the
inelastic scattering on Pr impurities yields an enhancement of the
superconducting transition temperature T$_c$ in LaOs$_{4}$Sb$_{12}$ and
increases monotonically as a function of Pr concentration. The calculated
results are in good agreement with the experimentally observed T$_c (x)$
dependence. Our analysis suggests that phonons and quadrupolar excitations
cause the attractive electron interaction which results in the formation of
Cooper pairs and singlet superconductivity in PrOs$_{4}$Sb$_{12}$.
