Profile Monitoring via Eigenvector Perturbation

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 (<i>ARL</i>₁) is an important challenge especially when the sampling rate is high and the control chart has an In-Control Average Run Length, called <i>ARL</i>₀, of 200 or more, as commonly found in practice. Unfortunately, arbitrary reduction of the FAR typically increases the <i>ARL</i>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 ARL1≈1 and ARL0&gt;106.