A comparison study of penalized likelihood via regularization and support vector-based control charts

ABSTRACT

Recently statistical process control (SPC) started incorporating advanced tools based on statistical learning for process monitoring due to the increasing availability of large and complex data sets. This phenomenon has generated new problems such as monitoring high-dimensional processes. Two well-known techniques used for this purpose are penalized likelihood and support vector-based process control charts. We investigate the support vector data description (SVDD), an effective method used in multivariate statistical process control (MSPC). Next, a least squares analogue to the SVDD, called LS-SVDD, is investigated. LS-SVDD is formulated using equality constraints in the underlying optimization problem which facilitates a fast, closed-form solution. Variable selection charts are penalized likelihood charts that use diagnosis methodologies for the identification of changed variables. Other penalized likelihood methods using Tikhonov regularization were proposed recently. This approach shrinks all process mean estimates towards zero rather than selecting variables, and it yields a closed-form solution of the monitoring statistic. In this article, we compare penalized methods and support vector methods for Shewhart-type and accumulative-type control charts.

KEYWORDS:

• One-class classification
• least squares support vector data description
• support vector data description
• average run length (ARL)

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Edgard Maboudou-Tchao

Edgard M. Maboudou-Tchao received his MSc and PhD in Statistics from the School of Statistics at the University of Minnesota, Twin Cities. He is currently a Full Professor of Statistics at the Department of Statistics & Data Science at the University of Central Florida. His work has been published in a variety of journals, including Technometrics, Journal of Quality Technology, Computational Statistics and Data Analysis and Journal of Applied Statistics. His research interests include: Statistical Learning Theory, Machine Learning, Data Science, One-Class Classification, Tensors, Multivariate Statistics, and Multivariate Statistical Process Control.

Charles W. Harrison

Charles W. Harrison received his MS in Statistical Computing and PhD in Big Data Analytics from the Department of Statistics & Data Science at the University of Central Florida. His PhD research advisor is Edgard M. Maboudou-Tchao. His research interests include tree-based machine learning, support vector methods, Bayesian statistics, and multivariate statistics.

Sumen Sen

Sumen Sen received his MS in Statisticlal Computing from the University of Central Florida. He received his PhD in Computational Mathematics from Old Dominion University, Norflok VA. Currently he is an associate professor at the Department of Mathematics and Statistics, Austin Peay State University, Clarksville, TN. His research interests include: Statistical Modeling, Machine Learning, Data Science.