Phase-II monitoring in multichannel profile observations

Abstract Process monitoring and fault diagnosis using profile data remains an important problem in statistical process control (SPC). It is particularly challenging with multichannel profiles. This article proposes a novel scheme for Phase-II monitoring of multichannel profiles. The proposed method integrates the exponentially weighted moving average (EWMA) scheme with multichannel functional principal component analysis (MFPCA) to obtain the charting statistics. Their control limits can be effectively computed by the Markov chain method. Moreover, we provide a natural diagnostic procedure to locate the possible change point once the chart is out-of-control. Our proposed method is demonstrated to be effective and efficient through simulation results and an industrial case study from a multioperation forging process.

[1]  Zachary G. Stoumbos,et al.  Robustness to Non-Normality of the Multivariate EWMA Control Chart , 2002 .

[2]  C.E. Shannon,et al.  Communication in the Presence of Noise , 1949, Proceedings of the IRE.

[3]  Hans-Georg Müller,et al.  Functional Data Analysis , 2016 .

[4]  Mahmoud A. Mahmoud,et al.  Statistical monitoring of multivariate multiple linear regression profiles in phase I with calibration application , 2010, Qual. Reliab. Eng. Int..

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

[6]  Fugee Tsung,et al.  A Multivariate Sign EWMA Control Chart , 2011, Technometrics.

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

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

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

[10]  Massimo Pacella,et al.  Profile monitoring via sensor fusion: the use of PCA methods for multi-channel data , 2014 .

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

[12]  Douglas M. Hawkins,et al.  Multivariate Exponentially Weighted Moving Covariance Matrix , 2008, Technometrics.

[13]  Fugee Tsung,et al.  LASSO-based multivariate linear profile monitoring , 2012, Ann. Oper. Res..

[14]  Douglas M. Hawkins,et al.  A Multivariate Change-Point Model for Statistical Process Control , 2006, Technometrics.

[15]  Marion R. Reynolds,et al.  A GLR Control Chart for Monitoring the Mean Vector of a Multivariate Normal Process , 2013 .

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

[17]  Shing I. Chang,et al.  On monitoring of multiple non-linear profiles , 2014 .

[18]  Fred Spiring,et al.  Introduction to Statistical Quality Control , 2007, Technometrics.

[19]  George C. Runger,et al.  A Markov Chain Model for the Multivariate Exponentially Weighted Moving Averages Control Chart , 1996 .

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

[21]  Peihua Qiu,et al.  A Change-Point Approach for Phase-I Analysis in Multivariate Profile Monitoring and Diagnosis , 2016, Technometrics.

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

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

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

[25]  A Santoro,et al.  On-line monitoring. , 1995, Nephrology, dialysis, transplantation : official publication of the European Dialysis and Transplant Association - European Renal Association.

[26]  Giovanna Capizzi,et al.  Practical Design of Generalized Likelihood Ratio Control Charts for Autocorrelated Data , 2008, Technometrics.

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

[28]  Zhisheng Zhang,et al.  Automatic Tonnage Monitoring for Missing Part Detection in Multi-Operation Forging Processes , 2010 .

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

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

[31]  H. Müller,et al.  Dynamical Correlation for Multivariate Longitudinal Data , 2005 .

[32]  Fugee Tsung,et al.  A generalized EWMA control chart and its comparison with the optimal EWMA, CUSUM and GLR schemes , 2003 .

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

[34]  Massimo Pacella,et al.  Monitoring and diagnosis of multichannel nonlinear profile variations using uncorrelated multilinear principal component analysis , 2013 .

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

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

[37]  Charles W. Champ,et al.  Effects of Parameter Estimation on Control Chart Properties: A Literature Review , 2006 .

[38]  Jane-ling Wang,et al.  Functional linear regression analysis for longitudinal data , 2005, math/0603132.

[39]  Douglas M. Hawkins,et al.  Self-Starting Multivariate Exponentially Weighted Moving Average Control Charting , 2007, Technometrics.

[40]  Sai Wang,et al.  The Monitoring of Linear Profiles with a GLR Control Chart , 2012 .