Online monitoring of autocorrelated multivariate linear profiles via multivariate mixed models

ABSTRACT

Multivariate multiple profile monitoring has been studied extensively over the past few years. Most of these studies assumed that the observations are uncorrelated, which could be violated in practice. In this paper, multivariate linear mixed model is proposed to allow correlation among observations of the multivariate multiple linear profiles. In order to monitor random effects and process variability in phase II, three control charts are suggested. The results of performance comparisons with an existing method show the superiority of the proposed control chart. Finally, the applicability of the proposed method is illustrated using a real case.

KEYWORDS:

• Multivariate exponential weighted moving average covariance (MEWMC) chart
• multivariate linear mixed model (MLMM)
• multivariate multiple linear profiles (MMLP)
• phase II
• within-profile correlation (WPC)

Disclosure statement

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

Additional information

Notes on contributors

Somayeh Khalili

Somayeh Khalili is a Ph.D. candidate in the Industrial Engineering Department at the Islamic Azad University - South Tehran Branch. She obtained her M.Sc. in Industrial Engineering from Qazvin Azad University and B.Sc. in Industrial Engineering from Amirkabir University of Technology, Tehran, Iran. Her current research interests include statistical quality control, statistical quality control and management in healthcare, machine learning and data science.

Rassoul Noorossana

Rassoul Noorossana is a professor of Applied Statistics in the Industrial Engineering Department at Iran University of Science and Technology. He received his BS in engineering from Louisiana State University in 1983 and MS and PhD in Engineering Management and Statistics from the University of Louisiana at Lafayette in 1986 and 1990, respectively. His primary research interests include statistical learning, process optimization, and statistical process control. He is a senior member of the American Society for Quality.