Multivariate Control Charts Based on Hybrid Novelty Scores

Abstract

We propose a new nonparametric multivariate control chart that integrates a novelty score. The proposed control chart uses as its monitoring statistic a hybrid novelty score, calculated based on the distance to local observations as well as on the distance to the convex hull constructed by its neighbors. The control limits of the proposed control chart were established based on a bootstrap method. A rigorous simulation study was conducted to examine the properties of the proposed control chart under various scenarios and compare it with existing multivariate control charts in terms of average run length (ARL) performance. The simulation results showed that the proposed control chart outperformed both the parametric and nonparametric Hotelling's T ² control charts, especially in nonnormal situations. Moreover, experimental results with real semiconductor data demonstrated the applicability and effectiveness of the proposed control chart. To increase the capability to detect small mean shift, we propose an exponentially weighted hybrid novelty score control chart. Simulation results indicated that exponentially weighted hybrid score charts outperformed the hybrid novelty score based control charts.

Keywords:

• Data mining
• Multivariate control charts
• Novelty score
• Quality control

Mathematical Subject Classification:

• 62P30
• 62H99

Acknowledgments

The authors would like to thank the editor and the reviewers for their useful comments and suggestions, which were greatly helpful in improving the quality of the article. This research was supported by Brain Korea 21 (Network Enterprise), Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science, and Technology (0003811), and the Ministry of Knowledge Economy in Korea under the IT R&D Infrastructure Program supervised by the NIPA (National IT Industry Promotion Agency) (NIPA-2011-(B1110-1101-0002)).