The Two-Inspector Problem

Reinspection is often used in industrial quality control as a final means of ensuring higher outgoing quality. Effectiveness is limited by the fault rate effect, which shows decreasing defect detection performance with successive stages of reinspection. This paper uses a model of the human inspector as a conservative signal detector to examine the various ways in which two inspectors can be combined to achieve enhanced system performance. An optimization program was used to select the optimum payoff matrix for each inspector and, given this optimum payoff matrix, various options were evaluated. It was concluded, as expected, that two inspectors are better than one and that better inspectors give better system performance. Other results were not so obvious. The method of combining the inspectors had only a 5% to 10°7o effect on system performance and the degree of conservatism of the two inspectors gave even smaller differences. The choice of inspection strategy was robust to changes in incoming product quality, provided the payoff matrix was optimized for each inspector.