Control charts for functional data based on functional mixture regression

Modern advanced data acquisition technologies have led to a massive increase in the collection of functional data or profiles to model quality char- acteristics in statistical process monitoring applications. Additional process variables, referred to as covariates, are also gathered, which potentially influence the quality characteristics and can be in scalar or functional form. Traditional functional linear models (FLMs) have proven effective, but they often fail to capture the intricate relationships between the quality characteristic and the covariates adequately. To address this limitation, an in- novative approach is proposed for profile monitoring, integrating functional mixture regression models to account for varying regression structures across different groups of subjects. The approach incorporates a multivariate functional principal component decomposition step to represent the functional data accurately. To evaluate its performance, a comprehensive Monte Carlo simulation study is conducted, comparing it with existing methods in the literature. Moreover, a real-case study from the automotive industry is presented to demonstrate the flexibility of the proposed approach in handling FLMs with diverse response types and predictors. The integrated approach showcases promising results and opens avenues for enhanced process analysis.