Nonparametric profile monitoring in multi-dimensional data spaces

Abstract Profile monitoring has received increasingly attention in a wide range of applications in statistical process control (SPC). In this work, we propose a framework for monitoring nonparametric profiles in multi-dimensional data spaces. The framework has the following important features: (i) a flexible and computationally efficient smoothing technique, called Support Vector Regression, is employed to describe the relationship between the response variable and the explanatory variables; (ii) the usual structural assumptions on the residuals are not required; and (iii) the dependence structure for the within-profile observations is appropriately accommodated. Finally, real AIDS data collected from hospitals in Taiwan are used to illustrate and evaluate our proposed framework.

[1]  Douglas C. Montgomery,et al.  Using Control Charts to Monitor Process and Product Quality Profiles , 2004 .

[2]  H. Künsch.  The Jackknife and the Bootstrap for General Stationary Observations , 1989 .

[3]  Yu Ding,et al.  Phase I Analysis for Monitoring Nonlinear Profiles in Manufacturing Processes , 2006 .

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

[5]  Corinna Cortes,et al.  Support-Vector Networks , 1995, Machine Learning.

[6]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[7]  A. B. Yeh,et al.  Bootstrap percentile confidence bands based on the concept of curve depth , 1996 .

[8]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

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

[10]  Stefania Mignani,et al.  Markov Chain Monte Carlo in Stastical Mechanics , 2001, Technometrics.

[11]  Mahmoud A. Mahmoud,et al.  On the Monitoring of Linear Profiles , 2003 .

[12]  Changliang Zou,et al.  A control chart based on a change-point model for monitoring linear profiles , 2006 .

[13]  Chih-Jen Lin,et al.  A Practical Guide to Support Vector Classication , 2008 .

[14]  Chih-Jen Lin,et al.  Asymptotic Behaviors of Support Vector Machines with Gaussian Kernel , 2003, Neural Computation.

[15]  R. Littell.  SAS System for Mixed Models , 1996 .

[16]  Rassoul Noorossana,et al.  Phase I Monitoring of Polynomial Profiles , 2008 .

[17]  Joseph P. Romano,et al.  The stationary bootstrap , 1994 .

[18]  Soumendra N. Lahiri,et al.  A nonparametric plug-in rule for selecting optimal block lengths for block bootstrap methods ☆ , 2007 .

[19]  Emily K. Lada,et al.  A wavelet-based procedure for process fault detection , 2002 .

[20]  Vasilis Z. Marmarelis,et al.  A Practitioner's Guide , 2004 .

[21]  Bernhard E. Boser,et al.  A training algorithm for optimal margin classifiers , 1992, COLT '92.

[22]  Willis A. Jensen,et al.  Profile Monitoring via Nonlinear Mixed Models , 2009 .

[23]  Massimo Pacella,et al.  On the use of principal component analysis to identify systematic patterns in roundness profiles , 2007, Qual. Reliab. Eng. Int..

[24]  P. Hall,et al.  On blocking rules for the bootstrap with dependent data , 1995 .

[25]  William H. Woodall,et al.  Statistical monitoring of nonlinear product and process quality profiles , 2007, Qual. Reliab. Eng. Int..

[26]  F. J. Pierce,et al.  Contemporary Statistical Models for the Plant and Soil Sciences , 2001 .

[27]  Su-Yun Huang,et al.  Model selection for support vector machines via uniform design , 2007, Comput. Stat. Data Anal..

[28]  William H. Woodall,et al.  Phase I Analysis of Linear Profiles With Calibration Applications , 2004, Technometrics.

[29]  Fugee Tsung,et al.  Monitoring General Linear Profiles Using Multivariate Exponentially Weighted Moving Average Schemes , 2007, Technometrics.

[30]  Bernhard Schölkopf,et al.  Support vector learning , 1997 .

[31]  W. Woodall,et al.  Statistical monitoring of heteroscedastic dose-response profiles from high-throughput screening , 2007 .

[32]  P. Bühlmann,et al.  Block length selection in the bootstrap for time series , 1999 .

[33]  Isabelle Guyon,et al.  Automatic Capacity Tuning of Very Large VC-Dimension Classifiers , 1992, NIPS.

[34]  Lan Kang,et al.  On-Line Monitoring When the Process Yields a Linear Profile , 2000 .

[35]  William H. Woodall,et al.  Current research on profile monitoring , 2007 .

[36]  Anthony C. Davison,et al.  Bootstrap Methods and Their Application , 1998 .

[37]  S. Lahiri.  Theoretical comparisons of block bootstrap methods , 1999 .

[38]  Willis A. Jensen,et al.  Monitoring Correlation Within Linear Profiles Using Mixed Models , 2008 .