Optimization designs of the combined Shewhart-CUSUM control charts

This article presents the optimization design of the combined Shewhart chart and CUSUM chart ( chart in short) used in Statistical Process Control (SPC). While the optimization design effectively improves the overall performance of the chart over the entire process shift range, it does not increase difficulties in understanding and implementing this combined chart. A new feature pertaining to an additional charting parameter w (the exponential of the sample mean shift) is also investigated, with the hope of further enhancing the detection effectiveness of the chart. Moreover, this article provides the SPC practitioners with a design table to facilitate the designs of the charts. From this design table, the users can directly find the optimal values of the charting parameters, according to the design specifications. The design table makes the design of an chart as simple as the design of the simplest chart. In general, this article will help to enhance the detection effectiveness of the chart, and facilitate and promote its applications in SPC.