基于单边假设检验的MEWMA控制图

MEWMA Control Chart Based on One-Sided Hypothesis Testing

摘要: 在过程参数的漂移方向已知的情况下，使用单侧控制图来检测过程参数的漂移比普通的控制图效果更好。现有的单边监控的方法主要分为两大类。第一类是简单地使用双侧控制图的单一控制限，仅监控感兴趣的一侧。第二类是采用数据截断的方法，将不相关一侧的观测值设为零，仅保留需要监控的一侧。本文提出了一种新的控制图，该控制图基于单边假设检验的似然比统计量，同时应用两个单边检验的统计量来监控多元正态分布均值向量的变化。单侧统计量的构建与应用，使得该控制图能够结合单侧控制图较为灵敏的优点，在过程参数漂移方向未知的情况下，也能基本达到漂移方向已知时的单侧控制图的监控效果。新的控制图结合了滑动窗口，能够聚焦于局部数据，从而更快速地捕捉过程中的微小变化。采用蒙特卡洛模拟方法计算了所提控制图的平均运行长度(ARL)。模拟结果表明，所提控制图比现有方法能更快地检测到偏移。

Abstract: When the direction of a process parameter shift is known in advance, using one-sided control charts to detect the shift is more effective than using traditional control charts. Existing methods for one-sided monitoring can be broadly classified into two categories. The first simply employs a single control limit from a two-sided chart to monitor the side of interest. The second adopts data truncation methods, where observations from the irrelevant side are set to zero, retaining only the side that requires monitoring. This paper proposes a novel control chart based on the likelihood ratio statistic for one-sided hypothesis testing, simultaneously applying two one-sided test statistics to monitor shifts in the mean vector of a multivariate normal distribution. The construction and application of these one-sided statistics enable the proposed chart to combine the sensitivity advantages of one-sided charts. Consequently, even when the direction of the process parameter shift is unknown, its monitoring performance is comparable to that of one-sided charts when the shift direction is known. The new chart incorporates a sliding window, allowing it to focus on local data and thereby capture small shifts in the process more quickly. The Average Run Length (ARL) of the proposed control chart was evaluated using Monte Carlo simulations. The simulation results demonstrate that the proposed chart detects shifts faster than existing methods.