Multivariate Process Variability Monitoring Through Projection

Abstract

Inspired by the recently developed projection chart, such as the U² chart for monitoring a shift in the multivariate mean, this article proposes a multivariate projection chart for monitoring process variability. In engineering practice, people often build a linear process model to connect the multivariate quality measurements with a set of fixed assignable causes. The column space of the process model naturally provides a subspace for projection and subsequent monitoring and was indeed used as the projection subspace in the recently developed projection control charts for monitoring a shift the mean. For the purpose of monitoring variability, however, we will show that such a projection may not be advantageous. We propose an alternative projecting statistic, labeled as VS, to be used for constructing a multivariate variability monitoring chart. We show, through extensive numerical studies, that the VS chart entertains several advantages over other competing methods, such as its less restrictive requirements on the process model and generally improved detection performance.

• Control Chart
• Generalized Variance
• Multivariate Process Variability
• Statistical Process Control

Additional information

Notes on contributors

Shuguang Hao

Mr. Shuguang Hao is a Graduate Student in the Department of Industrial and Systems Engineering. His email address is [email protected].

Shiyu Zhou

Dr. Shiyu Zhou is an Associate Professor in the Department of Industrial and Systems Engineering. His email address is [email protected]. He is the corresponding author.

Yu Ding

Dr. Yu Ding is an Associate Professor in the Department of Industrial and Systems Engineering. His email address is [email protected].