Multivariate control chart based on PCA mix for variable and attribute quality characteristics

Abstract

Two types of control charts exist based on different quality characteristics: variable and attribute. These characteristics are commonly monitored using separate procedures. Only a few studies focused on the utilization of control charts to monitor a process with mixed characteristics. This study develops a new concept of the $$T_{}^2$$ control chart based on a Principal Component Analysis (PCA) Mix, that is a PCA method that can jointly handle continuous and categorical data. The Kernel Density Estimation (KDE) method is used to estimate the control limit. Through simulation studies, the performance of the proposed chart is evaluated using the Average Run Length (ARL). $$\tilde T_{}^2$$ control limits obtained from KDE produce a stable ARL0 at ~ 370 for $$\alpha = 0.00273.$$ For the shifted process, the proposed chart demonstrates excellent performance for an appropriate number of principal components used. Applications of the simulated process and real cases show that the proposed chart is sensitive to monitoring the shifted process.

Keywords

• Mixed chart
• PCA mix
• T2 control chart
• kernel density estimation
• average run length