Designing New multivariate charting schemes for monitoring location under the classical and machine learning setups

This paper proposes two novel approaches that combines Multivariate Shewhart and Exponentially Weighted Moving Average (CMSEWMA) charts to monitor shifts in the location of multivariate data streams and integrating machine learning techniques. The methods are designed to effectively detect both large and small shifts in dynamic data streams, addressing the limitations of existing multivariate control charts. By fully utilizing the information from the out of control (OC) data and feeding both the original input and the input after applying the Multivariate Exponentially Weighted Moving Average (MEWMA) sequence into a Support Vector Machine (SVM) model, non-parametric monitoring statistics for large and small shifts are constructed, enhancing sensitivity to changes of different magnitudes. Extensive simulation studies and practical applications in water quality monitoring demonstrate that this control chart outperforms traditional methods, highlighting its robustness and adaptability under various data distributions and change conditions. The results validate the effectiveness of CMSEWMA control charts in detecting changes across diverse scenarios, making it a valuable tool for real-time monitoring in complex systems over competitors.