A bivariate CUSUM control chart based on exceedance statistics

In manufacturing systems, statistical process control (SPC) is used to detect unusual observations in the process. Most control charts are composed based on the normality assumptions of the observations. However, checking the normality assumption in multivariate control systems cannot be practical in real-life applications. As a result, we propose a nonparametric bivariate cumulative sum control chart (CUSUM) based on exceedance statistics for detecting the shifts in location parameters. Since the proposed chart (BCUSUM-EX) relied on exceedance statistics and is nonparametric, the use of the chart is straightforward and practical for users. Moreover, due to the nature of CUSUM charts, the proposed chart contains information about historical and current observations. The performance of the BCUSUM-EX chart is compared with the spatial sign CUSUM (SS-CUSUM) control chart under some well-known bivariate distributions such as bivariate normal, t, and gamma. The BCUSUM-EX chart's performance is better than the SS-CUSUM control chart regarding run length characteristics. Lastly, to show the importance of the proposed control chart, the BCUSUM-EX chart has been applied to the aluminium electrolytic capacitor manufacturing process.