Statistical monitoring of multivariate multiple linear regression profiles in phase I with calibration application

In some statistical process control applications, there are some correlated quality characteristics which can be modeled as linear functions of some explanatory variables. We refer to this structure as multivariate multiple linear regression profiles. When the correlation structure between quality characteristics is ignored and profiles are monitored separately then misleading results could be expected. Hence, developing methods to account for this multivariate structure is required. In this paper, we specifically focus on phase I monitoring of multivariate multiple linear regression profiles and develop four methods for this purpose. The performance of the developed methods is compared through simulation studies in terms of probability of a signal. In addition, a diagnostic scheme to find the out-of-control samples is developed. Finally, the application of the proposed methods is illustrated using a calibration application at the National Aeronautics and Space Administration (NASA) Langley Research Center. Copyright © 2009 John Wiley & Sons, Ltd.

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

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

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

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

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

[6]  Javier M. Moguerza,et al.  Monitoring Nonlinear Profiles Using Support Vector Machines , 2007, CIARP.

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

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

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

[10]  E. Smith.  Methods of Multivariate Analysis , 1997 .

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

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

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

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

[15]  P. Krishnaiah,et al.  Approximations to the Distributions of the Likelihood Ratio Statistics for Testing Certain Structures on the Covariance Matrices of Real Multivariate Normal Populations , 1975 .

[16]  A. Vaghefi,et al.  The effect of non-normality on performance of linear profile monitoring , 2008, 2008 IEEE International Conference on Industrial Engineering and Engineering Management.

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

[18]  William H. Woodall,et al.  Distribution of Hotelling's T2 Statistic Based on the Successive Differences Estimator , 2006 .

[19]  Abbas Saghaei,et al.  A CUSUM-based method for monitoring simple linear profiles , 2009 .

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[35]  R. Noorossana,et al.  Phase II Monitoring of Autocorrelated Polynomial Pro les in AR(1) Processes , 2010 .

[36]  E Memarzadeh Lotfabad,et al.  STRUCTURAL AND MAGNETIC STUDY OF ACTIVE SCREEN PLASMA NITRIDED FE73:5SI13:5B9NB3CU1 AND FE77SI11B9NB2:4CU0:6RIBBONS , 2010 .

[37]  Fugee Tsung,et al.  Using Profile Monitoring Techniques for a Data‐rich Environment with Huge Sample Size , 2005 .