Nonparametric Dynamic Curve Monitoring

<p>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.</p

A Distribution-Free Multivariate Control Chart

<div><p>Monitoring multivariate quality variables or data streams remains an important and challenging problem in statistical process control (SPC). Although the multivariate SPC has been extensively studied in the literature, designing distribution-free control schemes are still challenging and yet to be addressed well. This paper develops a new nonparametric methodology for monitoring location parameters when only a small reference dataset is available. The key idea is to construct a series of conditionally distribution-free test statistics in the sense that their distributions are free of the underlying distribution given the empirical distribution functions. The conditional probability that the charting statistic exceeds the control limit at present given that there is no alarm before the current time point can be guaranteed to attain a specified false alarm rate. The success of the proposed method lies in the use of data-dependent control limits, which are determined based on the observations on-line rather than decided before monitoring. Our theoretical and numerical studies show that the proposed control chart is able to deliver satisfactory in-control run-length performance for any distributions with any dimension. It is also very efficient in detecting multivariate process shifts when the process distribution is heavy-tailed or skewed. Supplementary materials for this article are available online.</p></div