Profile Monitoring via Eigenvector Perturbation

Abstract

In Statistical Process Control, control charts are often used to detect undesirable behavior of sequentially observed quality characteristics. Designing a control chart with desirably low False Alarm Rate (FAR) and detection delay ($AR{L}_1$) is an important challenge especially when the sampling rate is high and the control chart has an In-Control Average Run Length, called $AR{L}_0$, of 200 or more, as commonly found in practice. Unfortunately, arbitrary reduction of the FAR typically increases the $AR{L}_1$. Motivated by eigenvector perturbation theory, we propose the Eigenvector Perturbation Control Chart for computationally fast nonparametric profile monitoring. Our simulation studies show that it outperforms the competition and achieves both $AR{L}_1\approx 1$ and $AR{L}_0>10^6$.

Main: 19 pages, 3 figures. Supplemental: 24 pages, 9 figures This article has been accepted for publication in Technometrics, published by Taylor & Francis