Economic optimization of off-line inspection

In this paper we solve the problem of determining the optimal inspection/disposition policy for a finite batch of items produced by a machine that is subject to random breakdowns. In particular, we identify which units should be inspected and in which order so as to minimize costs. The operational implications of the optimal policy are analyzed with a selected set of numerical results. We place special emphasis on three different policies: the cost minimizing policy; the policy of perfect information, i.e., we insist on determining the quality of each unit; and the policy of zero-defects, i.e., we insist that all accepted units are known to conform to specifications, allowing the rejection of units of unknown quality. We also show how the optimal inspection/disposition policy is incorporated into the optimization of the batch size.