Control Charts for Monitoring Linear Profiles with Within-Profile Correlation Using Gaussian Process Models

Profile monitoring is the utilization of control charts for checking the stability of the quality of a product over time when the product quality is characterized by a function at each time point. Most existing control charts for monitoring profiles are based on the assumption that the observations within each profile are independent of each other, which is often invalid in practice. Successive measurements within profiles often exhibit spatial or serial correlation. This paper focuses on Phase II linear profile monitoring when within-profile data are correlated. A Gaussian process model is used to describe the within-profile correlation (WPC). Two Shewhart-type multivariate control charts are proposed to monitor the linear trend term and the WPC separately in Phase II. Our proposed approaches are compared with alternative methods through numerical simulations in which different in-control WPCs are considered. Simulation studies show that the proposed control charts are sensitive to changes in the linear trend term when the correlation is strong and effective in detecting large shifts in the WPC. Finally, an example is given to illustrate the implementation of our proposed control charts. Copyright © 2013 John Wiley & Sons, Ltd.

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

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

[3]  T. Choi,et al.  Gaussian Process Regression Analysis for Functional Data , 2011 .

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

[5]  Michael B. C. Khoo,et al.  Multivariate Control Chart for Process Dispersion Based on Individual Observations , 2003 .

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

[7]  Jyhwen Wang,et al.  Gaussian process method for form error assessment using coordinate measurements , 2008 .

[8]  A. Vaghefi,et al.  Phase II Monitoring of Nonlinear Profiles , 2009 .

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

[10]  Peter J. Diggle,et al.  An Introduction to Model-Based Geostatistics , 2003 .

[11]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[12]  Chien-Wei Wu,et al.  A multivariate EWMA control chart for monitoring process variability with individual observations , 2005 .

[13]  M. Shamsuzzaman,et al.  A combined control scheme for monitoring the frequency and size of an attribute event , 2010 .

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

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

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

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

[18]  Carl E. Rasmussen,et al.  Gaussian Processes for Machine Learning (GPML) Toolbox , 2010, J. Mach. Learn. Res..

[19]  Hannes Nickisch,et al.  The GPML Toolbox version 4 . 2 , 2016 .

[20]  Arthur B. Yeh,et al.  Multivariate Control Charts for Monitoring Covariance Matrix: A Review , 2006 .

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

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

[23]  Yang Zhang,et al.  Nonparametric control scheme for monitoring phase II nonlinear profiles with varied argument values , 2012 .

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

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

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

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

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

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

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

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