Phase I analysis of multivariate profiles based on regression adjustment

The use of statistical process control in monitoring and diagnosis of process and product quality profiles remains an important problem in various manufacturing industries. Although the analysis of profile data has been extensively studied in the literature, the challenges associated with monitoring and diagnosis of multiple functional profiles are yet to be well addressed because it is usually difficult to properly model the inter-relationship of multiple profiles. Motivated by a real-data application in semiconductor industries, we develop a new modelling and monitoring framework for Phase-I analysis of multiple profiles. The proposed framework incorporates the regression-adjustment technique into the functional principal component analysis. In this framework, the multiple profiles are treated as multivariate functional observations and their regression-adjusted residuals are used for monitoring. Simulation results show that the proposed method could describe the major structure of profile variation well and effectively find outlying profiles in a historical dataset due to sufficiently utilizing the information on between-profiles correlation.