Profile Monitoring via Eigenvector Perturbation

TL;DR

This paper introduces a fast, nonparametric profile monitoring control chart based on eigenvector perturbation theory, achieving low false alarms and rapid detection in high-frequency sampling scenarios.

Contribution

It proposes a novel eigenvector perturbation-based control chart that outperforms existing methods in speed and accuracy for profile monitoring.

Findings

Achieves $ARL_1$ close to 1, indicating rapid detection.

Maintains a high $ARL_0$ over 10^6, ensuring low false alarms.

Outperforms competing methods in simulation studies.

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 $ARL_0 > 10^6$.