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 $ARL_0 > 10^6$.

翻译：在统计过程控制中，控制图常用于检测顺序观测到的质量特征的不良行为。设计一个具有理想低误报率（FAR）和检测延迟（$ARL_1$）的控制图是一个重要的挑战，尤其是在采样率高且控制图具有受控平均运行长度（称为$ARL_0$）为200或更高的情况下，这在实践中很常见。不幸的是，任意降低FAR通常会增加$ARL_1$。受特征向量扰动理论的启发，我们提出了特征向量扰动控制图，用于计算快速的非参数轮廓监控。我们的模拟研究表明，它优于现有方法，并同时实现了$ARL_1 \approx 1$和$ARL_0 > 10^6$。