A new multivariate control chart for monitoring the quality of a process with the aid of auxiliary information

Abstract

Control chart is a statistical process control tool to routinely monitor the quality of a process. In the past decade, using auxiliary information to enhance the ability of control chart to detect parameter shifts has attracted wide attention in literature. Most of the existing works in this topic use a linear model and assume performance and auxiliary variables follow a bivariate normal distribution to establish the auxiliary-information-based (AIB) charts. However, the normality assumption could be violated on some occasions. In this study, the skew-normal distribution is used to characterize the auxiliary variable to expand the joint distribution of the performance and auxiliary variables to a generalized joint family. Then, a new multivariate AIB chart is established to monitor the quality of process. The performance of the proposed AIB control chart method is verified using Monte Carlo simulations. An example with regard to the cement filling process is used for illustration.

Keywords:

• Auxiliary information
• Hotelling ($T^2$) control chart
• non-normal distribution
• skew-normal distribution
• maximum likelihood estimator

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This study is supported by the grant of Ministry of Science and Technology, Taiwan MOST 108-2221-E-032-018-MY2 and the Fundamental Research Funds for the Central Universities of China Program No. JBK2001024.