Abstract

The great challenge in quality control is to devise computationally efficient algorithms to detect and diagnose process defects. Univariate statistical process control charts are currently used as an integral part in statistical quality control of engineering processes. Unfortunately, most data are inherently multivariate and need to be modelled accordingly. Major limitations such as higher data complexity and difficulty in interpretation have limited the application of multivariate techniques in process control. Motivated by the recent advances in dimensionality reduction algorithms and in order to effectively monitor highly correlated data, we introduce in this thesis new multivariate statistical process control charts based on the eigen-analysis of kernel matrices. The core idea behind our proposed techniques is to develop a theoretically rigorous methodology for multivariate statistical process control. We use scalp-recorded electroencephalograms (EEGs) as our real-world multivariate data source to demonstrate the effectiveness of our proposed algorithms. EEGs consist of vast amounts of complex data that require a trained professional to perform a proper analysis. Moreover, the currently used methodologies for analyzing EEGs are very labor-intensive. To circumvent these limitations, we show through extensive experimentation that our proposed approaches can be applied successfully in the analysis of EEGs by automating the detection of events. The task of classifying the events would still, however, be left to a professional clinician. For ease of visualization and analysis of EEGs, we designed a user-friendly Graphical User Interface (GUI) to test the performance of the proposed kernel dimension reduction techniques, and to also perform a comparison with the most prevalent methods used in multivariate process control