An Area‐based Methodology for the Monitoring of General Linear Profiles

Statistical profile monitoring has received much attention during recent years. While numerous contributions and applications have been demonstrated in the literature, the control statistics across many of the proposed methodologies have mainly remained unchanged, which somehow hinders further improvement of the monitoring schemes. In this paper, however, we propose a novel approach to leverage the information in the area formed between the sampled and in-control profile to improve the monitoring scheme performance. Specifically, we develop a control statistic based on the convolution of the observed and in-control profiles to monitor the shifts in the slope and intercept parameters. We also extend the mean square statistic to area weighted total sum of squares, to more effectively monitor the shift in the standard deviation. Extensive simulation studies are conducted to demonstrate the performance of the proposed methodology in comparison with some of the existing approaches. Copyright © 2016 John Wiley & Sons, Ltd.

[1]  Kamran Paynabar,et al.  Please Scroll down for Article Iie Transactions Characterization of Non-linear Profiles Variations Using Mixed-effect Models and Wavelets Characterization of Non-linear Profiles Variations Using Mixed-effect Models and Wavelets , 2022 .

[2]  Rassoul Noorossana,et al.  Phase II Monitoring of Nonlinear Profile Variance Using Wavelet , 2013, Qual. Reliab. Eng. Int..

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

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

[5]  Yang Zhang,et al.  Control Charts for Monitoring Linear Profiles with Within-Profile Correlation Using Gaussian Process Models , 2014, Qual. Reliab. Eng. Int..

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

[7]  Rassoul Noorossana,et al.  Change Point Estimation of Multivariate Linear Profiles Under Linear Drift , 2015, Commun. Stat. Simul. Comput..

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

[9]  Arthur B. Yeh,et al.  Profile monitoring for a binary response , 2009 .

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

[11]  Robert A. Kozak,et al.  Profile Charts for Monitoring Lumber Manufacturing Using Laser Range Sensor Data , 2007 .

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

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

[14]  P A Parker,et al.  A Single-Vector Force Calibration Method Featuring the Modern Design of Experiments , 2001 .

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

[16]  Carroll Croarkin.  Measurement Assurance for Dimensional Measurements on Integrated-Circuit Photomasks , 2018 .

[17]  Jianjun Shi,et al.  An SPC monitoring system for cycle-based waveform signals using haar transform , 2006, IEEE Transactions on Automation Science and Engineering.

[18]  A. Erhan Mergen,et al.  IMPROVING THE PERFORMANCE OF THE T2 CONTROL CHART , 1993 .

[19]  Sheng-Tsaing Tseng,et al.  Outlier detection in general profiles using penalized regression method , 2014 .

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

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

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

[23]  Douglas C. Montgomery,et al.  Some Statistical Process Control Methods for Autocorrelated Data , 1991 .

[24]  Peter A. Parker,et al.  Advancements in aircraft model force and attitude instrumentation by integrating statistical methods , 2007 .

[25]  Rassoul Noorossana,et al.  Phase II monitoring of multivariate multiple linear regression profiles , 2011, Qual. Reliab. Eng. Int..

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

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

[28]  Hang Zhang,et al.  Detecting outliers in complex profiles using a χ2 control chart method , 2009 .

[29]  Zhonghua Li,et al.  Control chart based on likelihood ratio for monitoring linear profiles , 2009, Comput. Stat. Data Anal..

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

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

[32]  Rassoul Noorossana,et al.  Monitoring polynomial profiles in quality control applications , 2009 .

[33]  Arthur B. Yeh,et al.  Phase I Control of Simple Linear Profiles with Individual Observations , 2013, Qual. Reliab. Eng. Int..

[34]  Rassoul Noorossana,et al.  Simple linear profiles monitoring in the presence of within profile autocorrelation , 2009, Comput. Ind. Eng..

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

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

[37]  Amirhossein Amiri,et al.  A case study on monitoring polynomial profiles in the automotive industry , 2009, Qual. Reliab. Eng. Int..

[38]  Rassoul Noorossana,et al.  Profile Monitoring Using Nonparametric Bootstrap T 2 Control Chart , 2012, Commun. Stat. Simul. Comput..

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

[40]  Amirhossein Amiri,et al.  Monitoring Correlated Profile and Multivariate Quality Characteristics , 2014, Qual. Reliab. Eng. Int..

[41]  Mahmoud A. Mahmoud,et al.  The Performance of Phase II Simple Linear Profile Approaches when Parameters Are Estimated , 2012, Commun. Stat. Simul. Comput..

[42]  Jye-Chyi Lu,et al.  Wavelet-based SPC procedure for complicated functional data , 2006 .

[43]  William H. Woodall,et al.  The monitoring of simple linear regression profiles with two observations per sample , 2010 .

[44]  Eric Chicken,et al.  Nonparametric Changepoint Estimation for Sequential Nonlinear Profile Monitoring , 2015, Qual. Reliab. Eng. Int..

[45]  Rassoul Noorossana,et al.  On the Monitoring of Autocorrelated Linear Profiles , 2008 .

[46]  Zhenyu Kong,et al.  High-dimensional process monitoring and change point detection using embedding distributions in reproducing kernel Hilbert space , 2014 .

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

[48]  Shing I. Chang,et al.  Statistical process control for monitoring non-linear profiles using wavelet filtering and B-Spline approximation , 2010 .

[49]  Jyh-Jen Horng Shiau,et al.  Effective Control Charts for Monitoring Multivariate Process Dispersion , 2012, Qual. Reliab. Eng. Int..

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

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

[52]  Shu-Kai S. Fan,et al.  Nonlinear Profile Monitoring of Reflow Process Data Based on the Sum of Sine Functions , 2013, Qual. Reliab. Eng. Int..

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

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

[55]  Erwin M. Saniga,et al.  Economic Statistical Control-Chart Designs With an Application to and R Charts , 1989 .

[56]  Mahmoud A. Mahmoud,et al.  Phase I Analysis of Multiple Linear Regression Profiles , 2008, Commun. Stat. Simul. Comput..

[57]  Jamal Arkat,et al.  A generalized linear statistical model approach to monitor profiles , 2007 .

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

[59]  Jianjun Shi,et al.  Automatic feature extraction of waveform signals for in-process diagnostic performance improvement , 2001, J. Intell. Manuf..

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

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

[62]  Sai Wang,et al.  A Generalized Likelihood Ratio Control Chart for Monitoring the Process Mean Subject to Linear Drifts , 2013, Qual. Reliab. Eng. Int..

[63]  Huairui Guo,et al.  Multiscale monitoring of autocorrelated processes using wavelets analysis , 2012 .

[64]  P. Moschopoulos,et al.  The distribution of the sum of independent gamma random variables , 1985 .

[65]  Douglas M. Hawkins,et al.  Zonation of multivariate sequences of digitized geologic data , 1974 .

[66]  Nan Chen,et al.  Bayesian hierarchical modeling for monitoring optical profiles in low-E glass manufacturing processes , 2015 .

[67]  Stelios Psarakis,et al.  SPC Procedures for Monitoring Autocorrelated Processes , 2007 .

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

[69]  Rassoul Noorossana,et al.  Phase II monitoring of multivariate simple linear profiles , 2010, Comput. Ind. Eng..

[70]  Stephen V. Crowder,et al.  An EWMA for Monitoring a Process Standard Deviation , 1992 .

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