A self-starting control chart for high-dimensional short-run processes

Abstract

A key challenge in using a traditional Hotelling’s chart with high-dimensionality measurements is that monitoring cannot begin until after the number of observations exceeds the dimensionality of the measurements, and the detection sensitivity to early shifts is reduced after that point until a substantial amount of observations has been accumulated. This is especially important with short-run processes where the measurements have high dimensionality. This article proposes a chart that allows monitoring with the second observation regardless of the dimensionality and reduces the average run length in detecting early shifts in high-dimensionality measurements. The proposed control chart can start monitoring quite early before considerable reference data are collected during the initial stage of production. A change point estimate is also available from our procedure, which is shown consistent for locating the correct change point. Both simulation results and an industry example show the effectiveness of the proposed control chart for monitoring short-run processes with high dimensionality.