In Part I tolerancing was discussed in general and statistical tolerancing in particular. Part II focused on general methods for determining the distribution of the response of a mechanism when the component tolerances are given distributions. Here in Part III cognizance is taken of the fact that the case of known distributions for the component tolerances is an idealization of what occurs in practice, i.e., the true tolerance distributions will shift and drift from the ideal ones. The several attacks known to the author which are aimed at being useful in practice are reviewed. While these methods provide insight, none is a panacea and this facet of statistical tolerancing remains troublesome. A delineation of some open problems and some general remarks conclude the paper.