监控profile数据的AMEWMA控制图

AMEWMA Control Chart for Monitoring Profile Data

摘要: 在线性轮廓数据的监控中，多变量指数加权移动平均(MEWMA)控制图因其对中、小漂移具有良好检测性能而被广泛研究。该控制图的监控性能依赖光滑参数的选取。然而，实际应用中过程漂移的大小通常是未知的，固定光滑参数往往难以同时兼顾不同幅度漂移的检测性能。因此，提出了一种自适应MEWMA控制图(AMEWMA^*)，基于控制图统计量构建漂移估计量${\widehat{\delta }}^{\ast }{}_t$ ，将光滑参数定义为权重函数$g({\widehat{\delta }}^{\ast }{}_t)$ ，从而实现光滑参数的自适应调整，引入RMI作为性能评价准则。通过统计模拟，对比了AMEWMA^*与AMEWMA、MEWMA及T²控制图的平均运行长度和RMI值，统计结果显示，AMEWMA^*的RMI值低于对比方法，说明其在小、中、大不同漂移场景下具有较快的响应速度。

Abstract: In the monitoring of linear profile data, the Multivariate Exponentially Weighted Moving Average (MEWMA) control chart has been extensively studied due to its strong detection capability for small to moderate process shifts. The monitoring performance of this control chart depends on the selection of the smoothing parameter. However, in practical applications, the magnitude of process shifts is typically unknown, and a fixed smoothing parameter often fails to balance detection performance across shifts of varying magnitudes. To address this limitation, an adaptive MEWMA control chart (AMEWMA^*) is proposed. By constructing a shift estimator ${\widehat{\delta }}^{\ast }{}_t$ based on the control chart statistic, the smoothing parameter is defined as a weight function $g\left({\widehat{\delta }}^{\ast }{}_t\right)$ , enabling adaptive adjustment of the smoothing parameter. Additionally, the Relative Monitoring Index (RMI) is introduced as a performance evaluation criterion. Through statistical simulations, AMEWMA is compared with AMEWMA, MEWMA, and T² control charts in terms of average run length and RMI values. The results demonstrate that AMEWMA^* achieves lower RMI values than the benchmark methods, indicating its enhanced responsiveness across small, moderate, and large shift scenarios.