Variable Selection-based Multivariate Cumulative Sum Control Chart

Abstract

High-dimensional applications pose a significant challenge to the capability of conventional statistical process control techniques in detecting abnormal changes in process parameters. These techniques fail to recognize out-of-control signals and locate the root causes of faults especially when small shifts occur in high-dimensional variables under the sparsity assumption of process mean changes. In this paper, we propose a variable selection-based multivariate cumulative sum (VS-MCUSUM) chart for enhancing sensitivity to out-of-control conditions in high-dimensional processes. While other existing charts with variable selection techniques tend to show weak performances in detecting small shifts in process parameters due to the misidentification of the 'faulty' parameters, the proposed chart performs well for small process shifts in identifying the parameters. The performance of the VS-MCUSUM chart under different combinations of design parameters is compared with the conventional MCUSUM and the VS-multivariate exponentially weighted moving average control charts. Finally, a case study is presented as a real-life example to illustrate the operational procedures of the proposed chart. Both the simulation and numerical studies show the superior performance of the proposed chart in detecting mean shift in multivariate processes.