Multivariate control charts for monitoring process mean vector of individual observations under regularized covariance estimation

ABSTRACT

Multivariate control charts are generally used in industries for monitoring and diagnosing processes characterized by several process variables. The applications of charts assume that the in-control process parameters are known and the charts’ limits are obtained from the known parameters. The parameters are typically unknown in practice, and the charts’ limits are usually based on estimated parameters from some historical in-control datasets in the Phase I study. The performance of the charts for monitoring future observation depends on efficient estimates of the process parameters from the historical in-control process. When only a few historical observations are available, the performance of the charts based on the empirical estimates of the process mean vector and covariance matrix have been shown to deviate from the desired performance of the charts based on the true parameters. We investigate the performance of the multivariate Shewhart control charts based on several shrinkage estimates of the covariance matrix when only a few in-control observations are available to estimate the parameters. Simulation results show that the control charts based on the shrinkage estimators outperform the charts based on existing classical estimators. An example involving high-dimensional monitoring is provided to illustrate the performance of the proposed Shrinkage-based Shewhart chart.

KEYWORDS:

• Average run length
• control charts
• covariance matrix
• high-dimensional monitoring
• shrinkage estimates

Acknowledgments

Open Access funding provided by the Qatar National Library.

Disclosure statement

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

Supplementary material

Supplemental data for this article can be accessed here.

Additional information

Notes on contributors

Olusola T. Omolofe

OLUSOLA T. OMOLOFE received the bachelor degree in Industrial Mathematics and Master's degree in Statistics from the Federal University of Technology, Akure, Nigeria. She is currently a Ph.D. student in the Department of Statistics, Federal University of Technology, Akure, Nigeria. 

Nurudeen A. Adegoke

NURUDEEN A. ADEGOKE received the Ph.D. degree in statistics from Massey University, Auckland, New Zealand. His current research interests include statistical process control, reliability, regularization procedures, and machine learning techniques. 

Olatunde A. Adeoti

Olatunde A. Adeoti obtained his B.Sc. degree (First class honours) in Mathematics from the University of Ilorin, M.Sc. Statistics from the University of Lagos and Ph.D. in Statistics from the University of Ilorin, Nigeria. He is a member of the Nigerian Statistical Association, American Society for Quality and the European Network for Business and Industrial Statistics. He is a recipient of the postdoctoral fellowship of the University of South Africa. He has articles that have been published in Quality Engineering, Quality and Reliability Engineering International, Communications in Statistics—Theory and Methods, International Journal of Quality and Reliability Management and Quality Technology and Quantitative Management. His research interest include Statistical Process Control, Artificial Neural Network in Statistical Process Control and StatisticalQuality Control and Management in Healthcare. He is currently an Associate Professor at the Department of Statistics, Federal University of Technology, Akure, Nigeria. His email address is [email protected]/[email protected]

Olusoga A. Fasoranbaku

OLUSOGA A.  FASORANBAKU received the Ph.D. degree in statistics from the University of Ibadan, Nigeria. He is currently a Professor with the Department of Statistics, Federal University of Technology, Akure, Nigeria. His research interests include econometrics, time series analysis and quality control.

Saddam Akber Abbasi

SADDAM AKBER ABBASI received the Ph.D. degree in statistics from The University of Auckland, New Zealand, in 2013. Before joining Qatar University, he was an Assistant Professor with the King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, for three years. He is currently working as an Assistant Professor with the Department of Mathematics, Statistics and Physics, Qatar University, Doha, Qatar. His research interests include SPC, time series analysis, profile monitoring, and non-parametric statistics.