A Least Angle Regression Control Chart for Multidimensional Data

In multidimensional applications, it is very rare that all variables shift at the same time. A statistical process control procedure would have superior efficiency when limited to the subset of variables likely responsible for the out-of-control conditions. The key idea of this article consists of combining a variable selection method with a multivariate control chart to detect changes in both the mean and variability of a multidimensional process with Gaussian errors. In particular, we develop a control chart for Phase II monitoring which integrates the least angle regression algorithm with a multivariate exponentially weighted moving average. Comparisons with related multivariate control schemes demonstrate the efficiency of the proposed control chart in a wide range of practical applications, including profile and multistage process monitoring. Further, the proposed scheme may also provide valuable diagnostic information for fault isolation. Supplemental materials, including an R package, are available online.