Mixed and adaptive memory control charts for process monitoring

Abstract

Control charts are statistical tools widely used to monitor changes in the parameters of production processes. The most popular control charts in practice are Shewhart, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA). The Shewhart control chart is considered sensitive to detect large shifts, whereas both the CUSUM and EWMA control charts are used to detect small-to-moderate shifts in a process location. To monitor both the small and large shifts simultaneously through a single control chart, several adaptive control charts have been suggested in the literature. However, most adaptive control charts approaches were designed only to monitor the process location. Thus improvements on the design structures of such control charts form the basis of this research. This study aims to develop adaptive control charts based on Huber and Bi-square functions as well as mixed control charts for efficient monitoring of the process location and dispersion parameters. The proposal includes the adaptive EWMA based on EWMA statistic, adaptive EWMA based on CUSUM statistic, and adaptive CUSUM based on CUSUM statistic. The other proposed charts are the mixed EWMA-CUSUM control chart to simultaneously monitor the process location and dispersion; and the mixed CUSUM-EWMA control charts for monitoring the dispersion of a process. There is also a multivariate extension of mixed CUSUM-EWMA which combines the design structures of the multivariate CUSUM and EWMA control charts. The statistical performances of the proposed control charts are evaluated using different performance measures. These performance measures include the average run length, standard deviation run length, extra quadratic loss, relative average run length, and performance comparison index. The results show that the proposed control charts are very effective in detecting wide range of shifts in the process locations and dispersion parameters. The graphical displays of statistical plots and operating curves show that the proposed charts significantly outperform most of the existing control charts. Interestingly, some existing control charts are special cases of the proposed control charts. Illustrative examples using real-life data are also given to demonstrate the practical importance and procedural details of the proposed methods.