A bivariate CUSUM control chart based on exceedance statistics

Abstract

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.

Enhanced Dispersion Monitoring Structures Based on Modified Successive Sampling: Application to Fertilizer Production Process

“…ARL 0 is defined as the ARL of the IC process, while ARL 1 is the ARL of an OOC process. In practice, the control limits of their corresponding charts are set against the pre-specified value of ARL 0 , and then the performance is evaluated based on the ARL 1 values [43,44]. It should be noted here that there are several short production runs with low-volume manufacturing environments where the quality of characteristics is monitored [45].…”

Nonparametric adaptive cumulative sum charting scheme for monitoring process location

“…Hou and Yu 14 developed an NPCUSUM shift detection chart for joint monitoring of the process parameters. Liang et al., 15 Song et al., 16 Graham, 17 Malela–Majika and Rapoo, 18 Li et al., 19 Abbas et al., 20 Erem and Mahmood 21 and the references therein may also be seen for more literature on these types of charting structures.…”