Predictive Analytics of Industrial Quality KPIs Using Scalable Gaussian Mixture Modeling

The Variational Inference Gaussian Mixture Model (VI-GMM) has been widely employed in multimode process modeling due to its inherent ability to automatically ascertain the optimal number of mixture components. Despite its advantages, the VI-GMM faces a significant computational challenge when dealing with large datasets, as it processes all data samples in each parameter update iteration. To address this issue, this paper introduces a novel approach: the Stochastic Variational Inference Gaussian Mixture Model (SVI-GMM). By leveraging the SVI algorithm to maximize the Evidence Lower Bound (ELBO), the scalability of the traditional VI-GMM is significantly enhanced, making it suitable for handling large- scale datasets. Furthermore, this study extends the application of SVI-GMM to its regression variant, SVI-GMR, for the forecasting of quality-related Key Performance Indicators (KPIs). The efficacy of the proposed methodology is demonstrated through a numerical example and a case study involving real-world industrial quality prediction modeling with extensive process data. These examples underscore the effectiveness and robustness of the SVI-GMM and SVI-GMR algorithms in providing accurate and scalable solutions for quality-related KPI predictions in big data environments.