In statistical tolerancing the tolerances on component parts of an assembly are specified as distributions. Allowance should be made for the fact that a distribution for a component may shift due to raw material variations, different suppliers, tool wear, and a myriad of other causes. We consider this problem for the simple case of a linear system with normal distributions which have known and fixed variances for the component tolerances; the component means are allowed to shift. We assume that the lots of incoming components are subjected to acceptance sampling by variables inspection and it is the purpose of this paper to relate the component tolerances and the sample sizes and levels of significance of the tests. An asymptotic expansion for the probability that an assembly will be out of specifications, which is derived elsewhere, and which rests on the pessimistic assumption that all possible component means for incoming lots are equally likely is explained and its use illustrated by example.