Auxiliary covariate-assisted condition monitoring for machinery

To ensure the safety of machines, condition monitoring is a fundamental tool for detecting anomalous or faulty events during operation. In the literature, Multivariate Statistical Process Control (MSPC) charts have been widely studied and applied as a baseline method for condition monitoring across various domains, such as manufacturing, power generation, and the chemical industry. However, the most of existing methods assume that the in-control distribution is fixed and not changed during the operation. In some applications, the in-control distribution of process variables may be influenced by some auxiliary covariates. These covariates are not the subjects to be controlled but provide useful information for a comprehensive understanding of the process variability. Although MSPC has been extensively studied in the literature, the heterogeneity in monitoring data from the covariates is still not well addressed. A novel monitoring scheme is proposed for multivariate heterogeneous processes with observable auxiliary covariates. The key idea is to convert the parameters in the classical hypothesis testing problem of MSPC into conditional expectations upon the observations of the covariate. In particular, we introduce a nonparametric methodology to link the in-control parameters with auxiliary covariates, which is highly flexible and extensible. The effectiveness of the proposed method is validated through numerical studies and two real-world case studies spanning diverse industrial scenarios. It indicates that accounting for heterogeneity can significantly enhance the performance of the control chart.