Monitoring General Linear Profiles When Random Errors Have Contaminated Normal Distributions

We consider the quality of a process which can be characterized by a general linear profile where the random error has a contaminated normal distribution. On the basis of trimmed least squares estimation, new control charts for monitoring the coefficient parameters and/or the error variance of the profile are proposed. Simulation studies show that the proposed control charts outperform the existing competitors under such a profile. An example from manufacturing facility is used to illustrate the applicability of the proposed charts. Copyright © 2013 John Wiley & Sons, Ltd.

[1]  S. Stigler Do Robust Estimators Work with Real Data , 1977 .

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

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

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

[5]  J. A. Robinson,et al.  Analysis of Variation Transmission in Manufacturing Processes—Part I , 1999 .

[6]  Changliang Zou,et al.  Profile Monitoring with Binary Data and Random Predictors , 2011 .

[7]  S. P. Wright,et al.  Comparing Curves Using Additive Models , 2002 .

[8]  Douglas C. Montgomery,et al.  Performance evaluation of two methods for online monitoring of linear calibration profiles , 2006 .

[9]  Mahmoud A. Mahmoud,et al.  A change point method for linear profile data , 2007, Qual. Reliab. Eng. Int..

[10]  E. L. Lehmann,et al.  Theory of point estimation , 1950 .

[11]  Chunguang Zhou,et al.  A Self-Starting Control Chart for Linear Profiles , 2007 .

[12]  Fugee Tsung,et al.  A distribution-free robust method for monitoring linear profiles using rank-based regression , 2012 .

[13]  Charles W. Champ,et al.  A multivariate exponentially weighted moving average control chart , 1992 .

[14]  Longcheen Huwang,et al.  On the Monitoring of Simple Linear Berkson Profiles , 2012, Qual. Reliab. Eng. Int..

[15]  D. Ruppert,et al.  Trimmed Least Squares Estimation in the Linear Model , 1980 .

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

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

[18]  George C. Runger,et al.  Designing a Multivariate EWMA Control Chart , 1997 .

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

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

[21]  R. Koenker,et al.  Regression Quantiles , 2007 .

[22]  Arthur B. Yeh,et al.  Profile monitoring for a binary response , 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]  Jianjun Shi,et al.  Stream of Variation Modeling and Analysis for Multistage Manufacturing Processes , 2006 .

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

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

[27]  Jionghua Jin,et al.  Feature-preserving data compression of stamping tonnage information using wavelets , 1999 .

[28]  Y. V. Hui,et al.  Monitoring an Input-Output Model for Production. I. The Control Charts , 1984 .

[29]  F. S. Stover,et al.  Statistical quality control applied to ion chromatography calibrations , 1998 .

[30]  Roger Koenker,et al.  Galton, Edgeworth, Frisch, and prospects for quantile regression in econometrics , 2000 .

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

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

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

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

[35]  Miloslav Suchánek,et al.  Multivariate control charts: Control charts for calibration curves , 1994 .

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