A Modified Robust Multivariate Monitoring Design Using The Principal Component Analysis Biplot

                                                                                          ABSTRACT

This research aims at developing a modified robust bootstrapped exploratory technique that are suitable for predictive monitoring of multivariate process datasets. Construction of robust traditional limits, robust principal component analysis (PCA), the bootstrap procedure, and biplot visualization, are the four core methodologies that are combined to develop novel techniques. Since the singular value decomposition (SVD) approach is known for handling rectangular datasets, and in addition, monitoring datasets are susceptible to outliers, correlations, and both short and long runs, the robust alternatives to the bootstrapped SVD becomes a contemporary scaffolding focus and thus, this births the robust bootstrapped SVD (RobBootSVD), with the robust properties beckoned on the sample Myriad estimate. The RobBootSVD in turn lead to a new robust bootstrapped PCA (RBPCA) algorithm and a corresponding RBPCA biplot model. In the application, a new suitable preliminary robust algorithm that utilizes the RobBootSVD and the Hoteling  was first developed to construct the needed robust contemporary limits that will serve as constraints during the monitoring stage. Hence, the new preliminary limits become a cornerstone for a user defined predictive monitoring regions, with  total regions upon which predictions could be made on  total variables, in an algorithm termed the RBPCA biplot monitoring (RBPCABM) configuration. Finally, the new RobBootSVD method outperforms the existing robust procedures that uses the mean and median estimates when appraised by the PCA biplot quality and Hoteling  monitoring. In the climax, the proposed RBPCABM approach revealed promising schemes that fostered multivariate quality decision making when evaluated with simulated and empirical datasets from a multinational tobacco manufacturing plant.