Monitoring Heterogeneous Multivariate Profiles Based on Heterogeneous Graphical Model

Abstract

Process monitoring using profile data remains an important and challenging problem in various manufacturing industries. Motivated by an application case of motherboard testing processes, we develop a novel modeling and monitoring framework for heterogeneous multivariate profiles. In this framework, a heterogeneous graphical model is constructed to depict the complicated heterogeneous relationship among profile channels. Then monitoring the heterogeneous relationship among profile channels can be reduced to monitoring the graphical networks. Besides, we investigate several theoretical results concerning the accuracy of the estimated graphical structure. Finally, we demonstrate the proposed method through extensive simulations and a real case study.

KEYWORDS:

• Heterogeneous graphical model
• Motherboard test processes
• Multivariate profiles
• Statistical monitoring

Supplementary Materials

Appendixes: A pdf file named “Appendixes” contains Appendices A and B, which are dedicated to proving Theorems 1 and 2, respectively.

R code: A zip file named “R code” contains codes and data used in this article.

Additional information

Funding

Research reported in this publication is supported by the National Natural Science Foundation of China under a key project (Grant No. 71731008) and the Beijing Natural Science Foundation (Grant No. L191022).