The Adaptive Exponentially Weighted Moving Average (AEWMA) chart, which combines the Shewhart and classical EWMA schemes, is usually designed using the Average Run Length ($\mathrm{A}RL$) as the criterion to be optimized. The shape of the run length distribution is known to change according to the magnitude of the shift in the process mean, ranging from highly skewed when the process is in-control or nearly to approximately symmetric when the shift is large. Therefore, the Median Run Length ($\mathrm{M}RL$) provides a more meaningful interpretation than the $\mathrm{A}RL$. In this paper, the $\mathrm{M}RL$ is used as an alternative performance criterion, and the AEWMA $\overline{X}$ chart is optimized for a wide range of mean shifts using zero and steady state modes. Comparative results show that the suggested AEWMA $\overline{X}$ chart offers a more balanced protection for detecting both small and large shifts in the process mean than the classical EWMA $\overline{X}$ chart, in terms of the $\mathrm{M}RL$ performance. The construction of the $\mathrm{M}RL$-based AEWMA $\overline{X}$ chart is also illustrated using an example, and it is compared with competing charts.

结合了Shewhart和经典EWMA方案的自适应指数加权移动平均值（AEWMA）图表通常使用平均游程长度（$\mathrm{一种}\mathrm{[R}\mathrm{大号}$）作为要优化的标准。已知行程长度分布的形状会根据过程平均值的变化幅度而变化，范围从过程处于受控状态时的高度偏斜到变化大时的近似对称。因此，中间游程长度（$\mathrm{中号}\mathrm{[R}\mathrm{大号}$）提供了比 $\mathrm{一种}\mathrm{[R}\mathrm{大号}$。在本文中，$\mathrm{中号}\mathrm{[R}\mathrm{大号}$ 被用作替代性能标准，而AEWMA $\overline{X}$该图表针对使用零和稳态模式的各种平均移位进行了优化。比较结果表明，建议的AEWMA$\overline{X}$ 与传统的EWMA相比，该图提供了更平衡的保护，可检测过程平均值中的大小变化 $\overline{X}$ 图表，就 $\mathrm{中号}\mathrm{[R}\mathrm{大号}$性能。的建设$\mathrm{中号}\mathrm{[R}\mathrm{大号}$基于AEWMA $\overline{X}$ 还通过示例说明了图表，并将其与竞争图表进行了比较。