In practice, a hybrid exponentially weighted moving average (HEWMA) control chart for monitoring the process mean based on the normality assumption. The performance of control chart is seriously affected if quality characteristics depart from normality or have the presence of outliers. For such situations, a new robust-HEWMA control chart is proposed for the scenario in which quality characteristics being monitored follow symmetric not necessarily normal as well as skewed phenomena. The generalized least-squares (GLS) algorithm based on order statistics is integrated to determine the control limits for non-normal process. Consequently, the process mean is unbiased and has the minimum variance in spite of non-normality. Moreover, for the long-tailed symmetric and skewed processes, the GLS estimators through their systematic coefficients structures provide robust estimates. To utilize this advantage, we have investigated the impact of data contamination and the estimators used in Phase I on the performance of proposed robust HEWMA control chart in the Phase II. Finally, we provide two real-life examples along with the simulation studies to show the implantation of our proposed chart.

在实践中，基于正态性假设的混合指数加权移动平均值（HEWMA）控制图用于监视过程平均值。如果质量特性偏离正常值或存在异常值，则会严重影响控制图的性能。在这种情况下，针对要监视的质量特性遵循对称（不一定是正常现象）和偏斜现象的情况，提出了一种新的鲁棒HEWMA控制图。集成了基于订单统计信息的广义最小二乘（GLS）算法，以确定非正常过程的控制极限。因此，过程平均值是无偏的，尽管存在非正态性，但方差最小。此外，对于长尾对称和偏斜过程，GLS估算器通过其系统系数结构提供了可靠的估算。为了利用这一优势，我们研究了第一阶段中数据污染和估计量对第二阶段中建议的健壮HEWMA控制图性能的影响。最后，我们提供了两个真实的例子以及仿真研究，以显示我们提出的图表的植入。