Monitoring simple linear profiles in the presence of generalized autoregressive conditional heteroscedasticity

In this paper, monitoring of simple linear profiles is investigated in the presence of nonequality of variances or heteroscedasticity, ie, generalized autoregressive conditional heteroscedasticity. In this condition, using of the common methods regardless of the heteroscedasticity leads to the fault interpretations. We consider a simple linear profile and assume that there is a generalized autoregressive conditional heteroscedasticity (GARCH) (1,1) model within the profiles. Here, we particularly focus on Phase II monitoring of simple linear regression. We studied the generalized autoregressive conditional heteroscedasticity effect, briefly GARCH effect, on the average run length criterion. As the remedial measures, the weighted least squares method to estimate the regression parameters and the heteroscedasticity‐consistent approaches to estimate the covariance matrix of regression parameters, are used to extract the GARCH effect. Two control chart methods namely T² and exponentially weighted moving average 3 are discussed to monitor the simple linear profiles. Their performances are evaluated by using the average run length criterion. Finally, a real case from an industry field is studied.