Lot streaming for quality control in two-stage batch production

We consider a two-stage batch manufacturing process in which the first stage shifts out-of-control at iid exponential times after starting in control. To improve quality, a production batch at Stage 1 is subjected to lot streaming: it is divided into sublots that are processed at Stage 1 and then passed one-by-one to Stage 2 for simultaneous inspection and processing. In any sublot, Stage 1 produces good items before the shift and bad items after. The state of Stage 1 is known as soon as a bad item is encountered in Stage 2, at which time Stage 1 is re-set to the in-control state. We examine both cases of continuous first-stage and continuous second-stage production. For each case we examine both LIFO and FIFO inspection and processing policies at Stage 2. We use nonlinear programming to develop lot streaming policies which minimize the expected number of defective items for LIFO and FIFO policies. We also develop simple approximately optimal policies and compare the output performance of optimal, approximately optimal and equal-lot policies (when applicable) in a numerical example.