Multivariate Exponentially Weighted Moving Average Control Charts Based On Copula And Its Performance Improvement

Control Chart is a key part of the statistical process control.It is widely used in industrial production to monitor product quality,and it plays an important role in machinery,electronics,chemical,metallurgy,and environmental industries.Modern industrial production processes often use the multivariate exponentially weighted moving average(MEWMA)control chart to monitor the in controll process for detecting the small shifts.Traditional MEWMA charts are built on the assumption of multivariate normal distribution,but many processes show non-normality and a certain correlation in reality.The Copulas are an effective tool to describe the correlation between random variables and to construct joint distribution function,therefore it is a good solution to this problem.This paper firstly establishes a multivariate exponentially weighted moving average control chart based on Copula joint distribution,and simulates the average run length under various conditions through Monte Carlo.The results show that when the downward shifts occur,its detection efficiency is poor.In order to improve the performance of the chart,to build a chart with higher detection efficiency and more robustness,we have tried two normal transformation methods.One is the Johnson transformation acting on univariate data,which turns each variable into a normal distribution and the correlation structure between variables is unchanged,then we can construct the Copula-MEWMA chart based on the transformation.The other is the Rosenblatt transformation acting on multivariate data,which can directly transform related non-normal variables into independent standard normal variables,which can be transformed into a traditional MEWMA charts.The simulation results show that the two transformed charts all outperform the original chart,they are more robust to different direction and different degree shifts.Among them,average run length of the out of control process is significantly reduced after Johnson transformation,its overall detection efficiency is the highest.Finally,a specific application of the above three charts are given by an example of the production of the aluminium electrolytic capacitor,which further proves the reliability of the theory.