Stream of variation modeling and monitoring for heterogeneous profiles in multi-stage manufacturing processes

Advanced manufacturing systems typically involve multiple operating stages, where in-process data are observed in the form of profiles that contain rich information for process monitoring. Emerging methodologies have been developed for multi-stage profile monitoring. However, the cases where different stages’ profiles are heterogeneous and variations propagate over stages have not been addressed so far. To this end, this article proposes a heterogeneous profiles-based stream of variation (HP-SoV) framework for multi-stage manufacturing process monitoring. It uses functional decomposition to extract features of heterogeneous profiles from different stages, where the decomposition coefficients are regarded as latent states that propagate along consecutive stages to capture the variation propagation. HP-SoV includes many existing models as its special cases, and enjoys an efficient inference algorithm via maximum likelihood estimation. Based on the one-step-ahead forecast errors of HP-SoV, a group monitoring scheme is further developed for online monitoring. Extensive numerical studies explore the modeling robustness and monitoring effectiveness of HP-SoV under different settings. A case study demonstrates the applicability of HP-SoV in multi-stage process monitoring for heterogeneous profiles.