Profile Monitoring via Linear Mixed Models

Profile monitoring is a relatively new technique in quality control used when the product or process quality is best represented by a profile (or a curve) at each time period. The essential idea is often to model the profile via some parametric method and then monitor the estimated parameters over time to determine if there have been changes in the profiles. Previous modeling methods have not incorporated the correlation structure within the profiles. We propose the use of linear mixed models to monitor the linear profiles in order to account for the correlation structure within a profile. We consider various data scenarios and show using simulation when the linear mixed model approach is preferable to an approach that ignores the correlation structure. Our focus is on Phase I control chart applications.