Monitoring Simple Linear Profile in the Presence of GARCH Effect

In many applications of statistical quality control, quality or performance of process is described by the relationship between a response variable and one or more independent variables that is called profile. The basic regression models or profile monitoring procedures assumes that error terms, ε_i’s , are uncorrelated random normal variables with zero mean and constant variance ( homosedasticity). In some applications, these assumptions are violated and lead to fault interpretations. In this paper, generalized autoregressive conditional heteroscedasticity effect, namely, GARCH effect on the monitoring of simple linear profiles are studied. We show the GARCH effect on the ARL (Average Run Length) criteria with simulation studies. As a remedial measure to remove these effects, we applied Box-Cox transformation. Simulation results show that the proposed method is able to remove the GARCH and ARCH effect.