A Multivariate Control Chart for SPC combining PCA and Radial Visualization Plots

A large number of processes nowadays are complex and characterized by the presence of several quality variables. In most cases these variables are interrelated and therefore the need arises to remove the correlation and reduce the dimensionality of the data, in order to efficiently control and monitor the process. The most popular approach towards this aim is Principal Component Analysis (PCA). PCA is a powerful mathematical tool that can assist analysis and monitoring of a process; this is termed Statistical Process Control (SPC) and in the presence of multiple variables, Multivariate SPC (MSPC). MSPC control charts based on PCA, usually take the form of either univariate or 2D / 3D plots, comprising Principal Components (PC), derived statistical quantities, based on PCA or combinations thereof. The current work presents a control chart for MSPC, based on the popular radial visualization Star Coordinates (SC) to plot process data, previously transformed using PCA. The main purpose of the chart is to identify samples with potential shifts. The identified outliers are then analyzed and the results are plotted in a second SC-based plot to identify the original causes of the shift.