Profile Monitoring via Nonlinear Mixed Models

Abstract

Profile monitoring is a relatively new technique in quality control best used where the process data follow a profile (or curve) at each time period. Little work has been done on the monitoring of nonlinear profiles. Previous work has assumed that the measurements within a profile are uncorrelated. To relax this restriction, we propose the use of nonlinear mixed models to monitor the nonlinear profiles in order to account for the correlation structure. We evaluate the effectiveness of fitting separate nonlinear regression models to each profile in Phase I control chart applications for data with uncorrelated errors and no random effects. For data with random effects, we compare the effectiveness of charts based on a separate nonlinear regression approach versus those based on a nonlinear mixed model approach. Our proposed approach uses the separate nonlinear regression model fits to obtain a nonlinear mixed model fit. Our studies show the nonlinear mixed model approach to be clearly superior to fitting separate nonlinear regression models. As a consequence, the nonlinear mixed model approach results in charts with good abilities to detect changes in Phase I data and has a simple-to-calculate control limit.