Optimization designs of the combined Shewhart-CUSUM control charts

This article presents the optimization design of the combined Shewhart chart and CUSUM chart (X¯&CUSUM chart in short) used in Statistical Process Control (SPC). While the optimization design effectively improves the overall performance of the X¯&CUSUM 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 ww (the exponential of the sample mean shift) is also investigated, with the hope of further enhancing the detection effectiveness of the X¯&CUSUM chart. Moreover, this article provides the SPC practitioners with a design table to facilitate the designs of the X¯&CUSUM 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 X¯&CUSUM chart as simple as the design of the simplest X¯ chart. In general, this article will help to enhance the detection effectiveness of the X¯&CUSUM chart, and facilitate and promote its applications in SPC.