Novel Nonparametric Control Charts For Monitoring Multivariate Processes
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The objective of this dissertation is to develop novel nonparametric control charts to effectively monitor and diagnose multivariate processes with a minimal set of modeling assumptions. Statistical process control (SPC) is a set of procedures that uses statistical techniques to measure, analyze, and reduce process variation. A control chart, which is a special type of graph showing the results of periodic inspections over time, is the primary and most successful SPC tool in real-world applications. This dissertation proposes two nonparametric multivariate control charts based on (1) a support vector machines (SVM) algorithm and (2) a linkage ranking algorithm. The first part of the dissertation proposes a new nonparametric multivariate control chart, called the SVM-PoC (Probability of Class) chart, which integrates a support vector machines algorithm, a bootstrap method, and a traditional control chart technique. SVM-PoC charts use the PoC values from an SVM algorithm as the monitoring statistic. The control limits of SVM-PoC charts are obtained in a nonparametric way that employs the percentile of the PoC values estimated by a bootstrap method. The performance of the proposed control charts are compared with multivariate Hotelling's T2 control charts, which are widely used, through a simulation study under various scenarios. The results show that the proposed SVM-based control charts outperform Hotelling's T2 control charts in both normal and nonnormal situations. The second part of the dissertation proposes a new nonparametric multivariate control chart based on a linkage ranking algorithm, a kLINK chart. This method constructs multivariate control charts based on the ranking of the new measurement relative to the training data. Simulations are performed to demonstrate the effectiveness of kLINK charts over Hotelling's T2 and ranking depth charts in nonnormal situations. Further, an exponential weighed moving average (EWMA) version of kLINK charts for increased sensitivity to small shifts was developed. The result showed that the EWMA-kLINK charts perform better than the original kLINK and multivariate exponentially weighted moving average (MEWMA) charts in detecting small shifts in the nonnormal cases.