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

Abstract

The products are commonly measured by two types of quality characteristics. The variable characteristics measure the numerical scale. Meanwhile, the attribute characteristics measure the categorical data. Furthermore, in monitoring processes, the multivariate variable quality characteristics may have a nonlinear relationship. In this paper, the Kernel PCA control chart is applied to monitor the mixed (attribute and variable) characteristics with the nonlinear relationship. First, the Average Run Length (ARL) is utilized to evaluate the performance of the proposed chart. The simulation studies show that the proposed chart can detect the shift in process. For this case, the Radial Basis Function (RBF) kernel demonstrates the consistent performance for several cases studied. Second, the performance comparison between the proposed chart and the conventional PCA Mix chart is performed. Based on the results, it is known that the proposed chart performs better in detecting the small shift in process. Finally, the proposed chart is applied to monitor the well-known NSL KDD dataset. The proposed chart shows good accuracy in detecting intrusion in the network. However, it still produces more False Negatives (FN).

Keywords

• Kernel PCA
• T2 Hotelling's chart
• Mixed quality characteristics
• Kernel Density Estimation
• Nonlinearity