Functional Graphical Models for Manufacturing Process Modeling

Abstract

Graphical models are widely used to model the statistical relationships among variables in a system. Existing graphical models can be used to model the relationships among scalar variables, but cannot be directly applied to model a system with functional variables. In this paper, a novel functional graphical model is proposed to model complex systems where functional variables are measured. To cope with the small sample size problem, we further develop a special sparsity penalization approach to robustly learn the graphical model from limited sample size, and develop a difference from the mean penalization for functional variables. Simulation studies and a case study in a plasma spray manufacturing process are used to demonstrate the effectiveness of the proposed method. Note to Practitioners —Emerging sensing and information technologies have provided unprecedented functional data collection capacity from systems over time. It is important and challenging to model the relationships among these variables. Among many different modeling alternatives, graphical models are powerful tools to characterize the underlying relationships among variables in systems. However, traditional graphical models cannot directly model a system with a mixture of functional and scalar variables. The proposed model aims to address this challenge by proposing a functional graphical model. Based on simulation studies and a case study for a plasma spray manufacturing process, it is shown that the proposed method performs well under various conditions.