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.

Keywords:

• Statistical process control
• control chart
• mixed-effects model
• sign chart
• meta-analysis
• Stouffer’s method
• high-dimensional data

Code availability

R code for a simple implementation of the proposed control chart and the simulation study of the Supplementary material is available at the Github website (https://github.com/yangdw01/MECCp.git).

Data availability statement

The data analyzed in this research will not be available to the public because of the information security policy of the company.

Additional information

Funding

This research was supported by research fund of Chungnam National University and Samsung Electronics Co., Ltd (IO201210-07968-01).

Notes on contributors

Daewon Yang

Daewon Yang is an assistant professor in the Department of Information Statistics at Chungnam National University. He obtained his Ph.D. degree in Statistics from Korea Advanced Institute of Science and Technology. Before joining Chungnam national university, he worked for 1 year and 6 months as a staff engineer at Samsung Electronics. His research interests include statistical process control, Bayesian Nonparametrics, Biostatistics, and high-dimensional data analysis.

Jinsu Park

Jinsu Park is an assistant Professor in the Department of Information Statistics at Chungbuk National University. He obtained his Ph.D. degree in Statistics from Korea Advanced Institute of Science and Technology. His research interests include Bayesian Nonparametrics, spatio-temporal model, and machine learning application in epidemiology.

Hayang Park

Hayang Park is an engineer at Samsung Electronics. His research interests include statistical process control, product engineering and generalized linear model.

Sungki Hong

Sungki Hong is a staff engineer at Samsung Electronics. His research interests include statistical process control, product engineering and clustering.

Jongmin Kim

Jongmin Kim is a principal engineer at Samsung Electronics. His research interests include statistical process control, product engineering and machine learning.

Seonghui Huh

Seong-Hui Huh is an executive vice president at Samsung Electronics. His research interests include statistical process control, product engineering and machine learning.

Eunkyung Kim

Eunkyung Kim is a vice president at Samsung Electronics. His research interests include statistical process control, product engineering and machine learning.

Jaeyong Jeong

Jaeyong Jung is a vice president at Samsung Electronics. His research interests include statistical process control and machine learning.

Yeonseung Chung

Yeonseung Chung is an Associate Professor in the Department of Mathematical Sciences at Korea Advanced Institute of Science and Technology. She obtained her Ph.D. degree in Biostatistics from University of North Carolina, Chapel Hill. Her research interests include Environmental Epidemiology, Bayesian Nonparametrics, and Biostatistics.