A mathematical model is developed for a quality control system for variables where the decision criteria may call for lot acceptance, lot screening, or lot scrapping. Since application of the quality control system may lead to one of three results, the model is termed three action. Exact and approximate conditions for optimality are developed. Conditions under which the optimum solution leads to one of the more conventional two action models (accept or screen, accept or scrap) are given. Application of the model and development of optimum solutions are illustrated by example.