Multi-stage change point detection with copula conditional distribution with pca and functional pca

A global uncertainty environment, such as the COVID-19 pandemic, has affected the manufacturing industry severely in terms of supply and demand balancing. So, it is common that one stage statistical process control (SPC) chart affects the next-stage SPC chart. It is our research objective to consider a conditional case for the multi-stage multivariate change point detection (CPD) model for highly correlated multivariate data via copula conditional distributions with principal component analysis (PCA) and functional PCA (FPCA). First of all, we review the current available multivariate CPD models, which are the energy test-based control chart (ETCC) and the nonparametric multivariate change point model (NPMVCP). We extend the current available CPD models to the conditional multi-stage multivariate CPD model via copula conditional distributions with PCA for linear normal multivariate data and FPCA for nonlinear non-normal multivariate data.