Multivariate Statistical Process Control Using LASSO

This paper 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 that it can select exactly the set of nonzero regression coefficients in multivariate regression modeling, which is especially useful in cases when the number of nonzero coefficients is small. In multivariate SPC applications, process mean vectors often shift in a small number of components. Our major goal is to detect such a shift as soon as it occurs and identify the shifted mean components. Using this connection between the two problems, a LASSO-based multivariate test statistic is proposed, which is then integrated into the multivariate EWMA charting scheme for Phase II multivariate process monitoring. It is shown that this approach balances protection against various shift levels and shift directions, and hence provides an effective tool for multivariate SPC applications.