Kernel principal component analysis (PCA) control chart for monitoring mixed non-linear variable and attribute...

Area of Science:

• Industrial Engineering
• Statistical Process Control
• Machine Learning

Background:

• Quality control involves monitoring variable (numerical) and attribute (categorical) data.
• Multivariate quality characteristics can exhibit complex nonlinear relationships.
• Existing methods may struggle with mixed data types and nonlinearities.

Purpose of the Study:

• To propose and evaluate a Kernel PCA control chart for monitoring mixed quality characteristics with nonlinear relationships.
• To assess the performance of the proposed chart using Average Run Length (ARL) and simulation studies.
• To compare the proposed chart with the conventional PCA Mix chart and apply it to a real-world dataset.

Main Methods:

• Application of Kernel PCA for dimensionality reduction and nonlinear relationship modeling.
• Utilizing Average Run Length (ARL) for performance evaluation.
• Simulation studies and application to the NSL KDD dataset for intrusion detection.

Main Results:

• The Kernel PCA control chart effectively detects process shifts.
• The Radial Basis Function (RBF) kernel showed consistent performance.
• The proposed chart demonstrated superior performance in detecting small process shifts compared to the conventional PCA Mix chart.
• The chart achieved good accuracy in detecting network intrusions on the NSL KDD dataset, though with some False Negatives.

Conclusions:

• The Kernel PCA control chart is a viable and effective tool for monitoring mixed quality characteristics with nonlinear relationships.
• It offers improved sensitivity for detecting small process shifts.
• Further refinement is needed to address False Negatives in network intrusion detection applications.