Robust Multivariate Control Chart Based on Goodness-of-Fit Test

Abstract

This paper proposes a distribution-free multivariate statistical process control (MSPC) chart to detect general distributional changes in multivariate process variables. The chart is deployed based on a multivariate goodness-of-fit test, which is extendible to high-dimensional observations. The chart also employs data-dependent control limits, which are computed on line along with the charting statistics, to ensure satisfactory and robust charting performance of the proposed method. Through theoretical and numerical analyses, we have shown that the proposed chart is exactly distribution-free and able to operate with an unknown in-control (IC) distribution or limited reference samples. The chart also has robust IC performance as well as satisfactory out-of-control (OC) detection power for general process changes without any assumption of the process distribution. A real-data example in semiconductor production processes is presented to demonstrate the application and effectiveness of our method.