A distribution-free monitoring technique for covariate-regulated processes

Process monitoring is crucial for ensuring the safe and reliable operation of equipment. Current process monitoring techniques often rely on distribution assumptions, such as the Gaussian distribution, which can be challenging to fulfill or justify in real-world applications. Moreover, many processes are influenced by exogenous covariates. While these covariates are not the primary focus of process monitoring, they offer valuable insights for a comprehensive understanding of process variability. To address these issues, we develop a distribution-free monitoring technique for covariate-regulated processes. Specifically, we propose a multivariate adaptive regression splines (MARS)-based quantile regression model. In contrast to traditional MARS techniques that employ a greedy search to include one pair of basis functions at each step, our approach involves incorporating all basis functions initially. This allows us to transform the problem into a linear programming and effectively incorporate constrains to avoid the quantile-crossing issue. Additionally, we introduce a three-level monitoring framework that progresses from monitoring single observations to quantile values and the entire quantile curves. We conduct numerical and real case studies to demonstrate the effectiveness of this technique.