Monitoring simple linear profiles in the presence of GARCH and non-normality effects

In some applications of statistical quality control, process quality is described by the relationship between a response variable and one or more explanatory variables that is called profile. Profile monitoring procedures assumes that error terms are uncorrelated random normal variables with zero mean and constant variance (homosedasticity). However in some applications, these assumptions can be violated and lead to fault interpretations. In this paper, generalized autoregressive conditional heteroscedasticity effect, namely, GARCH and non-normality distribution effect on the monitoring of simple linear profiles are studied. We show these effects on ARL (Average Run Length) criteria with simulation studies.