In this article, we first propose a new exponentially weighted moving average (EWMA ) chart for monitoring the shape parameter of the Weibull distribution. The proposed chart is developed based on the EWMA of the normal random variable, which is transformed from the easy‐to‐understand chi‐squared random variable. In contrast, the existing EWMA charts for monitoring the shape parameter use the sample range or the unbiased estimator of the shape parameter. Unfortunately, the EWMA chart generated from sample ranges is inefficient in detecting changes due to its lack of sufficiency, whereas the one produced using unbiased estimators of the shape parameter has a highly complicated distribution that is difficult to manipulate. Simulation studies are conducted to compare the effectiveness of the proposed EWMA chart and the two existing EWMA charts. Also, a maximum likelihood estimation method is employed to estimate the change point in the process for the proposed EWMA chart once an out‐of‐control (OC) signal has been triggered. Further, to reduce the time for detecting the OC signal, an EWMA chart with variable sampling intervals (VSIs) for monitoring the shape parameter is developed based on the proposed EWMA chart. This EWMA chart with VSIs is studied, and its performance is evaluated. Finally, an example to demonstrate the applicability and implementation of the proposed charts is provided.

中文翻译：

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用于监视Weibull形状参数的新EWMA控制图

在本文中，我们首先提出一个新的指数加权移动平均值（EWMA）图表，用于监视Weibull分布的形状参数。拟议的图表是基于正常随机变量的EWMA开发的，该图是从易于理解的卡方随机变量转换而来的。相反，用于监视形状参数的现有EWMA图表使用形状参数的样本范围或无偏估计量。不幸的是，由于缺乏足够的样本范围，从样本范围生成的EWMA图无法有效检测变化，而使用形状参数的无偏估计量生成的EWMA图具有高度复杂的分布，难以操作。进行仿真研究以比较建议的EWMA图表和两个现有EWMA图表的有效性。也，一旦触发了失控（OC）信号，将采用最大似然估计方法来估计拟议EWMA图的过程中的变化点。此外，为了减少检测OC信号的时间，基于提出的EWMA图，开发了具有可变采样间隔（VSI）的EWMA图，用于监视形状参数。研究了带有VSI的EWMA图表，并评估了其性能。最后，提供了一个示例来演示所建议图表的适用性和实现。基于提出的EWMA图，开发了具有可变采样间隔（VSI）的EWMA图，用于监视形状参数。研究了带有VSI的EWMA图表，并评估了其性能。最后，提供了一个示例来演示所建议图表的适用性和实现。基于提出的EWMA图，开发了具有可变采样间隔（VSI）的EWMA图，用于监视形状参数。研究了带有VSI的EWMA图表，并评估了其性能。最后，提供了一个示例来演示所建议图表的适用性和实现。