A sampling system, MIL-STD-105D, used in quality control consists of three sampling plans with different acceptance probabilities used in turn for lot inspection. The decision to switch plan is based on the history of the lot acceptance records and a set of stopping rules. We derive the performance measure, average outgoing quality (AOQ), of this sampling system from a renewal process in which AOQ is expressed in terms of the moments of the stopping times. The renewal approach is simpler than that of the Markov chain generally used in computing AOQ for an infinite sequence of lots; it also provides a formula for AOQ for a finite sequence of lots.