Nonparametric Dynamic Curve Monitoring

• Published in: Technometrics Vol. 60; no. 3; pp. 386 - 397
• Main Authors: Qiu, Peihua, Zi, Xuemin, Zou, Changliang
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 03.07.2018; American Society for Quality and the American Statistical Association; American Society for Quality
• Subjects: Adaptive control; Adaptive test; Control charts; Curve comparison; Data models; Design parameters; Dynamical systems; Estimating techniques; Generalized likelihood ratio test; Generalized linear models; Likelihood ratio; Model checking; Monitoring systems; Nadaraya-Watson kernel estimation; Noise monitoring; Nonparametric statistics; Statistical analysis; Statistical process control
• ISSN: 0040-1706; 1537-2723
• DOI: 10.1080/00401706.2017.1361340

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.