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.

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