In this study, a new process dispersion monitoring control chart is proposed based on a function-based adaptation to select the smoothing constant value, named as a function-based adaptive exponentially weighted moving average (EWMA) dispersion control chart. It is suggested to track shift ranges first expected in process dispersion by opting for smoothing constant computation with the help of a function. The shift magnitude assessment is made by an unbiased estimator that determines the smoothing constant value through the proposed function. The enhanced efficiency of the proposed chart can be assessed in terms of smaller run-length profiles, which are determined through Monte Carlo simulations. The proposed chart is compared with the existing adaptive EWMA dispersion chart, and it turned out to perform substantially efficiently in detecting all kinds of decreasing and increasing process dispersion shift magnitudes. Moreover, a real-life dataset application is explained in the example section to elaborate on the ease of implementation in the real-life scenario.

中文翻译：

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基于函数的自适应指数加权移动平均色散控制图

在这项研究中，提出了一种基于函数自适应选择平滑常数值的新过程离散监控控制图，称为基于函数的自适应指数加权移动平均（EWMA）离散控制图。建议通过在函数的帮助下选择平滑常数计算来跟踪过程分散中首先预期的偏移范围。偏移幅度评估由无偏估计器进行，该估计器通过建议的函数确定平滑常数值。可以根据更小的游程长度分布来评估拟议图表的增强效率，这些分布是通过蒙特卡罗模拟确定的。建议的图表与现有的自适应 EWMA 分散图表进行比较，事实证明，它在检测各种减少和增加的过程色散偏移幅度方面表现得非常有效。此外，示例部分还解释了一个现实生活中的数据集应用程序，以详细说明在现实生活场景中实施的难易程度。