Statistical process control (SPC) applies the science of statistics to various process control in order to provide higher-quality products and better services. The K chart is one among the many important tools that SPC offers. Creation of the K chart is based on Support Vector Data Description (SVDD), a popular data classifier method inspired by Support Vector Machine (SVM). As any methods associated with SVM, SVDD benefits from a wide variety of choices of kernel, which determines the effectiveness of the whole model. Among the most popular choices is the Euclidean distance-based Gaussian kernel, which enables SVDD to obtain a flexible data description, thus enhances its overall predictive capability. This thesis explores an even more robust approach by incorporating the Mahalanobis distance-based kernel (hereinafter referred to as Mahalanobis kernel) to SVDD and compare it with SVDD using the traditional Gaussian kernel. Method's sensitivity is benchmarked by Average Run Lengths obtained from multiple Monte Carlo simulations. Data of such simulations are generated from multivariate normal, multivariate Student's (t), and multivariate gamma populations using R, a popular software environment for statistical computing. One case study is also discussed using a real data set received from Halberg Chronobiology Center. Compared to Gaussian kernel, Mahalanobis kernel makes SVDD and thus the K chart significantly more sensitive to shifts in mean vector, and also in covariance matrix.
| Identifer | oai:union.ndltd.org:ucf.edu/oai:stars.library.ucf.edu:etd-2159 |
| Date | 01 January 2015 |
| Creators | Nguyen, Vu |
| Publisher | STARS |
| Source Sets | University of Central Florida |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Electronic Theses and Dissertations |
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