Detection of dependence shifts based on copula modeling for multivariate process monitoring

Enabled by Industry 4.0 advancements, such as intelligent sensors, the Internet of Things, and artificial intelligence, organizations are now able to efficiently collect process data through virtual metrology and use machine learning models to identify out-of-control processes. While existing research in multivariate process monitoring largely focuses on identifying mean and variance shifts, the growing importance of identifying dependence shifts in Industry 4.0 is evident, as the performance of machine learning-based monitoring critically depends on consistent dependence structures between training and monitored processes. Therefore, this study aims to propose a novel copula-based detection technique capable of identifying dependence shifts by integrating memory sign control charts for monitoring individual multivariate processes. This approach particularly leverages copula models to handle data that does not adhere to the multinormality assumption, making it essential for Industry 4.0, where virtual metrology replaces the physical one, eliminating the need for sampling. A large-scale Monte Carlo simulation study is then conducted to assess the run-length performance of the proposed framework against various dependence shift scenarios. The results demonstrate that the proposed framework outperforms traditional Highest Density Regions and classic Hotelling’s T2 in detecting specific dependence shift scenarios, even under the assumption of multinormality.