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 ($ARL_1$) is an important challenge especially when the sampling rate is high and the control chart has an In-Control Average Run Length, called $ARL_0$, of 200 or more, as commonly found in practice. Unfortunately, arbitrary reduction of the FAR typically increases the $ARL_1$. 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 $ARL_1 \approx 1$ and $ARL_0 > 10^6$.