Optimal inspection intervals in a two-stage manufacturing process

A strategy suggested recently in the literature for enhancing quality is to use inspection sublots, in which a large production run (batch) is subdivided into smaller portions (sublots) for inspection. In this study we consider a two-stage batch manufacturing process in which the first stage shifts out-of-control at i.i.d. exponential times after starting in control. In any sublot, Stage 1 produces good items before the shift and bad items after. As in a just-in-time environment, a shift's existence is detected when the operator at Stage 2 first encounters a bad item, at which point Stage 1 is re-set to the in-control condition. We use nonlinear programming to develop sublot sizes that maximize the expected number of good items produced by Stage 1. We consider both FIFO and LIFO processing at Stage 2.