Monitoring Correlation Within Linear Profiles Using Mixed Models

Profile monitoring is a relatively new set of techniques in quality control used when the product or process quality is best represented by a function (or a curve) at each time period. The 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 a correlation structure within the profiles. We propose the use of linear mixed models to monitor the linear profiles in order to account for any correlation structure within a profile. We conclude that, when the data are balanced, there appears to be no advantage in modeling correlation and/or including random effects because a simpler analysis that ignores the correlation structure will perform just as well as the more complicated analysis. When the data are unbalanced or when there are missing data, we find that the linear mixed model approach is preferable to an approach that ignores the correlation structure. Our focus is on Phase I control-chart applications.