Abstract: We investigate the problem of simultaneously inspecting shipments for variable sampling acceptance. Our goal is to simultaneously select all good shipments and exclude all bad shipments. By incorporating information from the samples taken from each of the shipments, an empirical Bayes simultaneous inspection procedure is proposed. The relative regret Bayes risk of is used as a measure of its performance. We have proved that the simultaneous inspection procedure is asymptotically optimal, and its relative regret Bayes risk converges to zero at rate .
Key words and phrases: Asymptotically optimal, empirical Bayes, rate of convergence, regret Bayes risk, simultaneous inspection, variable sampling acceptance.