Optimal adjustment strategies for a process with run-to-run variation and 0–1 quality loss

As short run manufacturing becomes more prevalent, run-to-run components of variation, such as that contributed by set-up error, have greater potential to crucially affect product quality. While efforts should be made to eliminate such between-run variance contributing factors, some will always be present. Here, we assume there is one such factor which we envisage as set-up error that, unless the process is adjusted, remains fixed throughout a run. We develop a single adjustment strategy based on taking a sample of fixed size from the process. If a significant set-up error is indicated, a single compensatory adjustment, equal to the predicted process offset, is executed. The actual procedure depends on process parameters, including adjustment error, run size, and adjustment and sampling costs. The procedure not only specifies the adjustment amount, if any, but the time during the run at which to adjust. The procedure is optimal among all fixed sample size procedures for the chosen cost function. Besides incorporting adjustment and sampling costs, the cost function is based on a 0–1 loss criterion, where the loss is 0 (1) unit per item produced if the process offset caused by set-up error is less than or equal to (greater than) a specified amount. Tables are provided, with examples, illustrating the procedure for representative values of process parameters, costs, and run sizes.