Multivariate Ordinal Categorical Process Control Based on Log-Linear Modeling

In many applications, the quality of products or services tends to be measured by multiple categorical characteristics, each of which is classified into attribute levels such as good, marginal, and bad. Here there is usually natural order among these attribute levels. However, traditional monitoring techniques ignore such order among them. By assuming that each ordinal categorical quality characteristic is determined by a latent continuous variable, this paper incorporates the ordinal information into an extended log-linear model and proposes a multivariate ordinal categorical control chart based on a generalized likelihood-ratio test. The proposed chart is efficient in detecting location shifts and dependence shifts in the corresponding latent continuous variables of ordinal categorical characteristics based on merely the attribute-level counts of the ordinal characteristics.

[1]  Douglas C. Montgomery,et al.  A review of multivariate control charts , 1995 .

[2]  Hassen Taleb,et al.  Control charts applications for multivariate attribute processes , 2009, Comput. Ind. Eng..

[3]  Fugee Tsung,et al.  Recursive parameter estimation for categorical process control , 2010 .

[4]  J. Chiu,et al.  Attribute Control Chart for Multivariate Poisson Distribution , 2007 .

[5]  G. Geoffrey Vining,et al.  CUSUM Charts for Monitoring the Characteristic Life of Censored Weibull Lifetimes , 2014 .

[6]  Jian Li,et al.  Directional Control Schemes for Multivariate Categorical Processes , 2012 .

[7]  Shelby J. Haberman,et al.  Log-Linear Models for Frequency Tables with Ordered Classifications , 1974 .

[8]  A. Agresti.  Analysis of Ordinal Categorical Data: Agresti/Analysis , 2010 .

[9]  P. McCullagh.  Analysis of Ordinal Categorical Data , 1985 .

[10]  C. F. Jeff Wu,et al.  Experiments: Planning, Analysis, and Parameter Design Optimization , 2000 .

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

[12]  Stephen E. Fienberg,et al.  Discrete Multivariate Analysis: Theory and Practice , 1976 .

[13]  Fugee Tsung,et al.  Run-to-Run Process Adjustment Using Categorical Observations , 2007 .

[14]  W. Woodall,et al.  Multivariate CUSUM Quality- Control Procedures , 1985 .

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

[16]  Charles W. Champ,et al.  The Performance of Exponentially Weighted Moving Average Charts With Estimated Parameters , 2001, Technometrics.

[17]  Fugee Tsung,et al.  A spatial rank‐based multivariate EWMA control chart , 2012 .

[18]  Fugee Tsung,et al.  Multivariate binomial/multinomial control chart , 2014 .

[19]  Fugee Tsung,et al.  Rank-based process control for mixed-type data , 2016 .

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

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

[22]  Stelios Psarakis,et al.  Review of multinomial and multiattribute quality control charts , 2009, Qual. Reliab. Eng. Int..

[23]  Luigi Salmaso,et al.  Nonparametric Permutation-Based Control Charts for Ordinal Data , 2014 .

[24]  Kwok-Leung Tsui,et al.  A Control Chart Method for Ordinal Data , 2002 .

[25]  T. W. Anderson.  An Introduction to Multivariate Statistical Analysis, 2nd Edition. , 1985 .

[26]  Stelios Psarakis,et al.  Multivariate statistical process control charts: an overview , 2007, Qual. Reliab. Eng. Int..

[27]  H. I. Patel.  QUALITY CONTROL METHODS FOR MULTIVARIATE BINOMIAL AND POISSON DISTRIBUTIONS , 1973 .

[28]  Thong Ngee Goh,et al.  CONTROL CHART FOR MULTIVARIATE ATTRIBUTE PROCESSES , 1998 .

[29]  Fugee Tsung,et al.  A simple categorical chart for detecting location shifts with ordinal information , 2014 .

[30]  O. Vorobyev,et al.  Discrete multivariate distributions , 2008, 0811.0406.

[31]  Anja Vogler,et al.  An Introduction to Multivariate Statistical Analysis , 2004 .