An optimization design of the combined Shewhart-EWMA control chart

Abstract

This article presents an optimization design of the combined Shewhart $\overline{X}$ chart and exponentially weighted moving average (EWMA) chart ($\overline{X}$&EWMA chart in short) used in statistical process control (SPC). The design algorithm not only optimizes the charting parameters of the $\overline{X}$ chart and EWMA chart, but also optimizes the allocation of detection power between the two charts’ elements, based on the loss function, so that the best overall performance can be achieved. The optimization design is carried out under the constraints on the false alarm rate and available resources. While the optimization design effectively improves the overall performance of the $\overline{X}$&EWMA chart over the entire process shift range, it does not increase the difficulty of understanding and implementing this combined chart. A 2^k factorial experiment shows that the optimal $\overline{X}$&EWMA chart outperforms the main competitor, the basic $\overline{X}$&EWMA chart, by about 50 %, on average. Moreover, this article provides the SPC practitioners with a design table to facilitate the designs of the $\overline{X}$&EWMA charts. From this design table, the users can directly find the optimal values of the charting parameters according to the design specifications.