Research On Heteroscedasticity And Correlation Of Data Based On Control Chart

The main tool for statistical process control is control charts,EWMA control charts are one of the most commonly used control charts.The EWMA control chart is unitary,and only one quality characteristic value can be monitored.Based on this,a multi-element EWMA control chart-MEWMA control chart has been developed.The conventional MEWMA control chart requires our observations to be independent of each other and follow the same distribution,but in real production life,some data do not meet these conditions.Many data have heteroscedasticity and cannot be directly monitored by control charts,There is also a correlation between some data,but we want to monitor the correlation of the data using control charts.Therefore,for these situations,we study the control chart and propose two methods,which can monitor the multivariate data with heteroscedasticity and correlation,and can detect whether the correlation between random variables has changed.In this context,this article has done the following two work on control charts:First,The GARCH model is introduced on the basis of the traditional MEWMA control chart,The GARCH model can well describe the Heteroscedasticity of random variables.First use the GARCH model to fit the heteroscedasticity of each random variable separately,and then use the conditional heteroscedasticity of the fitted GARCH model to replace the unconditional variance of the random variable,use this as the respective variance in the covariance matrix of the MEWMA control chart statistics,and then use the MEWMA control chart to monitor the multiple random variables.The simulation results show that the GARCH type MEWMA control chart can monitor the data with heteroscedasticity very well.Second,this paper proposes a new method for multivariate data correlation testing.Copula function and Kendall 's tau characterize the coordination of changes in multiple random variables,and measure the correlation between random variables.We use the relationship between Kendall 's tau and Copula parameters ,using Kendall 's tau,we can get the value of the Copula parameter ,then we use the EWMA chart to monitor Copula parameters .On the one hand,the monitoring of Kendall 's tau is transformed into the monitoring of Copula parameters,which meets the prerequisite of the control chart requiring the observations to be independent and identically distributed;On the other hand,the monitoring of Copula parameters can reflect whether the correlation between random variables has changed.It is also a new method for validating Copula parameters,because when the correlation of random variables changes,the original Copula parameters will no longer apply.The results show that our method works well.