Multivariate Statistical Process Control Using LASSO

Abstract

This article develops a new multivariate statistical process control (SPC) methodology based on adapting the LASSO variable selection method to the SPC problem. The LASSO method has the sparsity property of being able to select exactly the set of nonzero regression coefficients in multivariate regression modeling, which is especially useful in cases where the number of nonzero coefficients is small. In multivariate SPC applications, process mean vectors often shift in a small number of components. Our primary goals are to detect such a shift as soon as it occurs and to identify the shifted mean components. Using this connection between the two problems, we propose a LASSO-based multivariate test statistic, and then integrate this statistic into the multivariate EWMA charting scheme for Phase II multivariate process monitoring. We show that this approach balances protection against various shift levels and shift directions, and thus provides an effective tool for multivariate SPC applications. This article has supplementary material online.

Keywords:  :

• Hotelling’s T² statistic
• Model selection
• Multivariate statistical process control
• Penalized likelihood
• Regression-adjusted variable