Nonparametric Dynamic Curve Monitoring

ABSTRACT

Rapid sequential comparison between the longitudinal pattern of a given subject and a target pattern has become increasingly important in modern scientific research for detecting abnormal activities in many data-rich applications. This article focuses on this problem when observations are collected sequentially with uncorrelated or correlated noise involved. A dynamic monitoring procedure is developed after connecting the curve monitoring problem to curve comparison. Under the framework of generalized likelihood ratio testing, we suggest a new exponentially weighted moving average (EWMA) control chart that can accommodate unequally spaced design points. An adaptive parameter selection feature is built in the proposed control chart so that the chart can detect a wide range of longitudinal pattern shifts effectively. To furnish fast computation, recursive formulas are derived for computing the charting statistic. Numerical studies show that the proposed method can deliver a satisfactory performance, and it outperforms existing methods in various cases. An example from the semiconductor manufacturing industry is used for the illustration of its implementation. Supplementary materials for this article are available online.

KEYWORDS:

• Adaptive test
• Curve comparison
• Generalized likelihood ratio test
• Model checking
• Nadaraya–Watson kernel estimation
• Statistical process control

Supplementary Materials

The supplementary material contains some technical details, additional simulation results.

Acknowledgments

The authors thank the editor, the associate editor, and two anonymous referees for many helpful comments that have resulted in significant improvements in the article.

Additional information

Funding

This research was supported by NNSF of China Grants