Robust control chart based on mixed-effects modeling framework: A case study in NAND flash memory industry

Abstract

In this research, we analyze the real data in the NAND Flash memory industry using a control chart. There are thousands of electrical measures for each NAND Flash memory chip. We monitor these data through a control chart to ensure that the manufacturing process is in control. For better interpretability, we apply a univariate control chart technique to each variable. However, most existing control charts, such as the EWMA chart, do not include between-subgroup variations but only within-subgroup variations. They often obtain too narrow control limits for some variables, which leads too many subgroups to fall outside the control limits. To overcome this issue, we apply a control chart under a mixed-effects modeling framework to include both within-subgroup and between-subgroup variations. Additionally, the EWMA chart assumes that all the items are normally distributed; however, we frequently encounter that a normal assumption is violated. To overcome this limitation, we apply a robust approach based on a nonparametric sign chart. Furthermore, we introduce a p-value combination method to increase the statistical power for the gradual change detection of a statistical process. Our study show that the proposed control chart can efficiently monitor the real data in the NAND Flash memory industry.