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.

[1]  Fugee Tsung,et al.  Monitoring Profiles Based on Nonparametric Regression Methods , 2008, Technometrics.

[2]  David J. Spiegelhalter,et al.  Statistical methods for healthcare regulation: rating, screening and surveillance , 2012 .

[3]  P. Qiu.  Image processing and jump regression analysis , 2005 .

[4]  Dongdong Xiang,et al.  Surveillance of cardiovascular diseases using a multivariate dynamic screening system , 2015, Statistics in medicine.

[5]  S. Steiner.  EWMA Control Charts with Time-Varying Control Limits and Fast Initial Response , 1999 .

[6]  Giovanna Capizzi,et al.  Adaptive Generalized Likelihood Ratio Control Charts for Detecting Unknown Patterned Mean Shifts , 2012 .

[7]  Giovanna Capizzi,et al.  An Adaptive Exponentially Weighted Moving Average Control Chart , 2003, Technometrics.

[8]  Colin O. Wu,et al.  Nonparametric Mixed Effects Models for Unequally Sampled Noisy Curves , 2001, Biometrics.

[9]  Herbert Moskowitz,et al.  Run-Length Distributions of Special-Cause Control Charts for Correlated Processes , 1994 .

[10]  Jeffrey D. Hart,et al.  Nonparametric Smoothing and Lack-Of-Fit Tests , 1997 .

[11]  W. H. Deitenbeck.  Introduction to statistical process control. , 1995, Healthcare facilities management series.

[12]  Changliang Zou,et al.  CONTROL CHART FOR MONITORING NONPARAMETRIC PROFILES WITH ARBITRARY DESIGN , 2009 .

[13]  Rassoul Noorossana,et al.  Statistical Analysis of Profile Monitoring , 2011 .

[14]  Shi-Shang Jang,et al.  Monitoring Batch Processes with Multiple On–Off Steps in Semiconductor Manufacturing , 2011 .

[15]  D. Hawkins,et al.  NONPARAMETRIC CONTROL CHART FOR MONITORING PROFILES USING CHANGE POINT FORMULATION AND ADAPTIVE SMOOTHING , 2009 .

[16]  James M. Lucas,et al.  Exponentially weighted moving average control schemes: Properties and enhancements , 1990 .

[17]  Karen A. F. Copeland.  Cumulative Sum Charts and Charting for Quality Improvement , 1999 .

[18]  Stefan H. Steiner.  Exponentially Weighted Moving Average Control Charts with Time-Varying Control Limits and Fast Initial Response , 1998 .

[19]  Jianqing Fan,et al.  Generalized likelihood ratio statistics and Wilks phenomenon , 2001 .

[20]  Snigdhansu Chatterjee,et al.  Distribution-free cumulative sum control charts using bootstrap-based control limits , 2009, 0906.1421.

[21]  Dongdong Xiang,et al.  Univariate Dynamic Screening System: An Approach For Identifying Individuals With Irregular Longitudinal Behavior , 2014, Technometrics.

[22]  Zhang Wu,et al.  An SPRT control chart with variable sampling intervals , 2011 .

[23]  K. B. Kulasekera.  Comparison of Regression Curves Using Quasi-Residuals , 1995 .

[24]  Fugee Tsung,et al.  A Reference-Free Cuscore Chart for Dynamic Mean Change Detection and a Unified Framework for Charting Performance Comparison , 2006 .

[25]  Giovanna Capizzi,et al.  A Least Angle Regression Control Chart for Multidimensional Data , 2011, Technometrics.

[26]  Stephen E. Fienberg,et al.  Discussion on the paper by Spiegelhalter, Sherlaw-Johnson, Bardsley, Blunt, Wood and Grigg , 2012 .

[27]  Joel L. Horowitz,et al.  An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model Against a Nonparametric Alternative , 2001 .

[28]  Peter Hall,et al.  Bootstrap test for difference between means in nonparametric regression , 1990 .

[29]  D. Hawkins,et al.  Cumulative Sum Charts and Charting for Quality Improvement , 1998, Statistics for Engineering and Physical Science.

[30]  Peihua Qiu,et al.  Nonparametric Profile Monitoring by Mixed Effects Modeling , 2010, Technometrics.

[31]  H. Müller,et al.  Local Polynomial Modeling and Its Applications , 1998 .

[32]  Rassoul Noorossana,et al.  Statistical Analysis of Profile Monitoring: Noorossana/Profile Monitoring , 2011 .

[33]  Daniel W. Apley,et al.  The dynamic T 2 chart for monitoring feedback-controlled processes , 2002 .

[34]  Wei Jiang,et al.  A Weighted CUSUM Chart for Detecting Patterned Mean Shifts , 2008 .

[35]  Long Feng,et al.  Local Walsh-average regression , 2012, J. Multivar. Anal..

[36]  Eric Chicken,et al.  Statistical Process Monitoring of Nonlinear Profiles Using Wavelets , 2009 .

[37]  Wenceslao González-Manteiga,et al.  An updated review of Goodness-of-Fit tests for regression models , 2013, TEST.