LASSO-based diagnosis scheme for multistage processes with binary data

Abstract Process monitoring using multistage processes with binary data remains an important and challenging problem in statistical process control (SPC). Although the multistage processes has been extensively studied in the literature, the challenges associated with designing diagnostic schemes when only binary responses are observed are yet to be addressed well. This paper develops a practical LASSO-based diagnostic procedure which combines BIC with the popular adaptive LASSO variable selection method. Given the oracle property of LASSO and its algorithm, the diagnostic result can be obtained easily and quickly. More importantly, the proposed method does not require making any extra tests that are necessary in existing diagnosis methods. Numerical and real-data examples demonstrate the effectiveness of our method.

[1]  Liangsheng Qu,et al.  Evolving kernel principal component analysis for fault diagnosis , 2007, Comput. Ind. Eng..

[2]  Arthur B. Yeh,et al.  Monitoring the covariance matrix via penalized likelihood estimation , 2013 .

[3]  Trevor Hastie,et al.  Regularization Paths for Generalized Linear Models via Coordinate Descent. , 2010, Journal of statistical software.

[4]  J. Nelder,et al.  Double hierarchical generalized linear models (with discussion) , 2006 .

[5]  Joseph J. Pignatiello,et al.  IDENTIFYING THE TIME OF A STEP-CHANGE WITH X 2 CONTROL CHARTS , 1998 .

[6]  Fugee Tsung,et al.  Statistical process control for multistage processes with binary outputs , 2013 .

[7]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[8]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[9]  William H. Woodall,et al.  Change-point detection of mean vector or covariance matrix shifts using multivariate individual observations , 2000 .

[10]  W. T. Tucker,et al.  Identification of out of control quality characteristics in a multivariate manufacturing environment , 1991 .

[11]  Jianjun Shi,et al.  Causation-Based T2 Decomposition for Multivariate Process Monitoring and Diagnosis , 2008 .

[12]  J. E. Jackson.  Multivariate quality control , 1985 .

[13]  Chuen-Sheng Cheng,et al.  Using neural networks to detect the bivariate process variance shifts pattern , 2011, Comput. Ind. Eng..

[14]  Edgard M. Maboudou-Tchao,et al.  Monitoring the covariance matrix with fewer observations than variables , 2013, Comput. Stat. Data Anal..

[15]  H. Zou.  The Adaptive Lasso and Its Oracle Properties , 2006 .

[16]  Joseph J. Pignatiello,et al.  DIAGNOSING SIGNALS FROM T 2 AND χ2 MULTIVARIATE CONTROL CHARTS , 1998 .

[17]  Fugee Tsung,et al.  False Discovery Rate-Adjusted Charting Schemes for Multistage Process Monitoring and Fault Identification , 2009, Technometrics.

[18]  R. Tibshirani,et al.  On the “degrees of freedom” of the lasso , 2007, 0712.0881.

[19]  Lifeng Xi,et al.  Fault diagnosis in assembly processes based on engineering-driven rules and PSOSAEN algorithm , 2011, Comput. Ind. Eng..

[20]  F. Ahmadzade,et al.  Identifying the time of a step change with MEWMA control charts by artificial neural network , 2008, 2008 IEEE International Conference on Industrial Engineering and Engineering Management.

[21]  Joseph J. Pignatiello,et al.  IDENTIFYING THE TIME OF A STEP-CHANGE WITH X 2 CONTROL CHARTS , 1998 .

[22]  Wei Jiang,et al.  An adaptive T 2 chart for multivariate process monitoring and diagnosis , 2009 .

[23]  Joe H. Sullivan,et al.  Detection of Multiple Change Points from Clustering Individual Observations , 2002 .

[24]  Charles W. Champ.  Multivariate Statistical Process Control with Industrial Applications , 2004 .

[25]  Fugee Tsung,et al.  A Variable-Selection-Based Multivariate EWMA Chart for Process Monitoring and Diagnosis , 2012 .

[26]  Tai-Yue Wang,et al.  Artificial neural networks to classify mean shifts from multivariate χ2 chart signals , 2004, Comput. Ind. Eng..

[27]  Peng Zhao,et al.  On Model Selection Consistency of Lasso , 2006, J. Mach. Learn. Res..

[28]  R. Gueorguieva,et al.  A multivariate generalized linear mixed model for joint modelling of clustered outcomes in the exponential family , 2001 .

[29]  Fugee Tsung,et al.  Directional MEWMA Schemes for Multistage Process Monitoring and Diagnosis , 2008 .

[30]  Jianqing Fan,et al.  Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties , 2001 .

[31]  Edgard M. Maboudou-Tchao,et al.  A LASSO Chart for Monitoring the Covariance Matrix , 2013 .

[32]  J. Nelder,et al.  Hierarchical Generalized Linear Models , 1996 .

[33]  K. Tsui,et al.  Identification and Quantification in Multivariate Quality Control Problems , 1994 .

[34]  John C. Young,et al.  Multivariate statistical process control with industrial applications , 2002, ASA-SIAM series on statistics and applied probability.

[35]  John C. Young,et al.  A Practical Approach for Interpreting Multivariate T2 Control Chart Signals , 1997 .

[36]  Fugee Tsung,et al.  A Change Point Approach for Phase I Analysis in Multistage Processes , 2008, Technometrics.

[37]  Robert L. Mason,et al.  Step-Down Analysis for Changes in the Covariance Matrix and Other Parameters , 2007 .

[38]  Youngjo Lee,et al.  Comparison of hierarchical and marginal likelihood estimators for binary outcomes , 2004, Comput. Stat. Data Anal..

[39]  D. Hawkins.  Multivariate quality control based on regression-adjusted variables , 1991 .

[40]  Peihua Qiu,et al.  Multivariate Statistical Process Control Using LASSO , 2009 .

[41]  Youn Min Chou,et al.  Applying Hotelling's T2 Statistic to Batch Processes , 2001 .

[42]  Yuhong Yang.  Can the Strengths of AIC and BIC Be Shared , 2005 .

[43]  Dariusz Ceglarek,et al.  Diagnosability Analysis of Multi-Station Manufacturing Processes , 2002 .

[44]  Nola D. Tracy,et al.  Decomposition of T2 for Multivariate Control Chart Interpretation , 1995 .

[45]  Yong Chen,et al.  Diagnosability Study of Multistage Manufacturing Processes Based on Linear Mixed-Effects Models , 2003, Technometrics.

[46]  Daniel W. Apley,et al.  A Factor-Analysis Method for Diagnosing Variability in Mulitvariate Manufacturing Processes , 2001, Technometrics.

[47]  Arthur B. Yeh,et al.  Monitoring multivariate process variability with individual observations via penalised likelihood estimation , 2012 .

[48]  Wei Jiang,et al.  A context tree method for multistage fault detection and isolation with applications to commercial video broadcasting systems , 2009 .

[49]  S. Bersimis,et al.  IDENTIFYING THE OUT OF CONTROL VARIABLE IN A MULTIVARIATE CONTROL CHART , 2002 .

[50]  Wei Jiang,et al.  A LASSO-Based Diagnostic Framework for Multivariate Statistical Process Control , 2011, Technometrics.