An optimization design of the 3-EWMA scheme for monitoring mean shifts

Abstract

This article presents an algorithm for the optimization design of the three exponentially weighted moving average control chart scheme (3-EWMA scheme in short) for monitoring a range of mean shifts. The design algorithm optimizes the charting parameters of the 3-EWMA scheme, based on extra quadratic loss function. The results of comparative studies and an example show that the optimal 3-EWMA scheme always outperforms the basic 3-EWMA scheme, as well as the other EWMA charts under different specifications. According to a 2k factorial experiment, the optimal 3-EWMA scheme outperforms the main competitor, the basic 3-EWMA scheme, by more than 15 %, on average. Although the design of the optimal 3-EWMA scheme is more difficult than that of the conventional EWMA charts, it can be easily computerized. Moreover, this article provides the statistical process control (SPC) practitioners with a design table to facilitate the designs of the 3-EWMA schemes. From this design table, the users can directly find the optimal values of the charting parameters according to the design specifications. In general, this article will help to enhance the detection effectiveness of the 3-EWMA scheme, and facilitate its applications in SPC.