Statistica Sinica 10(2000), 953-969

SIMULTANEOUS INSPECTION FOR VARIABLE

SAMPLING ACCEPTANCE

TaChen Liang

Wayne State University

Abstract: We investigate the problem of simultaneously inspecting $k$ 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 $k$ shipments, an empirical Bayes simultaneous inspection procedure $\oalign{\hbox{$\delta$}\crcr\hidewidth \vbox to.2ex{\hbox{\char'176}\vss}\hidewidth}^{*}$ is proposed. The relative regret Bayes risk of $\oalign{\hbox{$\delta$}\crcr\hidewidth \vbox to.2ex{\hbox{\char'176}\vss}\hidewidth}^{*}$ is used as a measure of its performance. We have proved that the simultaneous inspection procedure $\oalign{\hbox{$\delta$}\crcr\hidewidth \vbox to.2ex{\hbox{\char'176}\vss}\hidewidth}^{*}$ is asymptotically optimal, and its relative regret Bayes risk converges to zero at rate $O\left( k^{-1}\ell n^{2}k\right)$.

Key words and phrases: Asymptotically optimal, empirical Bayes, rate of convergence, regret Bayes risk, simultaneous inspection, variable sampling acceptance.