Multi-Task Learning With Latent Variation Decomposition for Multivariate Responses in a Manufacturing Network

Modeling the relationships between the quality response variables and process settings or in situ sensing variables is a fundamental problem in quality engineering. Such relationships are important for product quality prediction, process monitoring, and optimization. Data collected from a single system often only carry limited information, making modeling one system at a time challenging. Multi-task learning (MTL) jointly models similar-but-non-identical systems and utilizes the similarities among systems for better performance. However, existing MTL becomes much less effective if important variables are missing or unmeasurable in the underlying process (latent variables). More importantly, commonly shared latent variables across systems often reflect important process patterns/behaviors, deserving more investigations. We proposed an MTL framework for multivariate or profile responses by explicitly decomposing the variation among systems into explainable variation and latent variation. Specifically, the explainable variation is from variables observed in data, while the latent variation is from the latent basis functions automatically generated from model residuals. The proposed method improves the prediction accuracy and interpretability of modeling. The simulation and a case study in a silicon ingot manufacturing network demonstrate that the proposed method can improve the quality modeling performance and recover critical process knowledge for silicon ingot manufacturing based on Czochralski (CZ) process. Note to Practitioners—This research is motivated by quality modeling of a semiconductor manufacturing network consisting of multiple furnaces (systems) producing silicon ingots. An accurate quality model in manufacturing is essential for downstream tasks such as process monitoring and optimization. As data collected from a single system often only carry limited information, aggregating data from multiple systems in quality modeling can significantly improve the performance. However, different systems in a network are often similar-but-non-identical to each other due to different degradation statuses, usage history, product receipts. As a result, data from different systems are heterogeneous, making combining all data for modeling inappropriate. Multi-task learning (MTL) solves this problem and recovers the similar-but-non-identical nature of systems. However, existing MTL is much less effective if important latent factors/variables are missing or unmeasurable in the underlying process. More importantly, such latent factors can reflect important process patterns/behaviors. This work improves the MTL framework by explicitly explaining the unexplained variations using the latent factors automatically generated from model residuals. The simulation and the case study in a silicon ingot manufacturing network demonstrate that the proposed method improves the quality modeling performance and recovers critical process knowledge for silicon ingot manufacturing based on Czochralski (CZ) process.