Multi-Stage Change Point Detection with Copula Conditional Distribution with PCA and Functional PCA

Jong-Min Kim,Yumin Liu,Ning Wang

doi:10.3390/math8101777

Abstract

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.

Highlights

Since Hotelling (1949) proposed Hotelling T 2 statistics for the multivariate statistical process control (SPC), Crosier (1988), Lowry, Woodall, Champ and Rigdon (1992), and Zou and Tsung (2011) have proposed the multivariate versions of the cumulative sum (CUSUM) time-weighted control chart and the exponentially weighted moving average (EWMA) time-weighted SPCs
With the simulated multivariate data, we found that the functional PCA (FPCA)-based conditional multi-stage multivariate
We proposed the conditional multi-stage multivariate change point detection (CPD) method by employing principal component analysis (PCA) or FPCA, copula conditional distribution, and the multivariate CPD models, which are energy test-based control chart (ETCC) and the nonparametric multivariate change point model (NPMVCP)

Summary

Introduction

Since Hotelling (1949) proposed Hotelling T 2 statistics for the multivariate statistical process control (SPC), Crosier (1988), Lowry, Woodall, Champ and Rigdon (1992), and Zou and Tsung (2011) have proposed the multivariate versions of the cumulative sum (CUSUM) time-weighted control chart and the exponentially weighted moving average (EWMA) time-weighted SPCs. the manufacturing industry is still requiring a modern statistical technique dealing with non-normal high dimensional correlated multivariate data. Over the last two decades, Reference [3,4,5] developed the change point detection (CPD) models with needed pre-knowledge for in-control distribution and nonparametric CPD charts to detect mean, variance, and other distributional shifts. Reference [6] proposed online nonparametric multivariate CPD models. Reference [7] reviewed previous works focusing on energy divergence

Objectives

Methods

Conclusion