In this talk we explore the problem of determining the optimal inspection/disposition policy for a finite batch of items produced by a machine which is subject to random breakdowns. This talk will explore two separate, but related works. In the first work, we investigate situations in which the disposition of some of the units can and should be made without unquestionably identifying their status. In the second we apply information theory to the problem of finding the first nonconforming unit in the batch at minimum cost.