Identifying the time of a step change with multivariate single control charts

Abstract

Change point estimation procedures simplify the efforts to search for and identify special causes in multivariate statistical process monitoring. After a signal is generated by the simultaneously used control charts or a single control chart, add-on change point procedure estimates the time of the change. In this study, multivariate joint change point estimation performance for simultaneous monitoring of both location and dispersion is compared under the assumption that various single charts are used to monitor the process. The change detection performance for several structural changes for the mean vector and covariance matrix is also discussed. It is concluded that choice of the control chart to obtain a signal may affect the change point detection performance.

Keywords:

• Hotelling's T² control chart
• generalized variance control chart
• change point estimation
• maximum-likelihood estimation
• multivariate single control charts

Mathematics Subject Classification:

• 62P30
• 62H12

Acknowledgements

Dogu's research was partially funded by the grants from the graduate scholarship program of the Scientific and Technological Research Council of Turkey (TUBITAK). The author thanks the editor, the associate editor, and the referee for careful reading and for their comments which greatly improved the paper. The author also thanks Dr Ipek Deveci Kocakoc for her support and guidance throughout the research