Investigating the problem of setting control limits for an exponentially weighted moving average (EWMA) chart in the case of parameter uncertainty is more accessible when monitoring the variance because only one parameter has to be estimated. Simply ignoring the induced uncertainty frequently leads to control charts with poor false alarm performances. Adjusting the unconditional in-control (IC) average run length (ARL) makes the situation even worse. Guaranteeing a minimum conditional IC ARL with some given probability is another very popular approach to solving these difficulties. However, it is very conservative as well as more complex and more difficult to communicate. We utilize the probability of a false alarm within the planned number of points to be plotted on the control chart. It turns out that adjusting this probability produces notably different limit adjustments compared to controlling the unconditional IC ARL. We then develop numerical algorithms to determine the respective modifications of the upper and two-sided EWMA charts based on the sample variance for normally distributed data. These algorithms are made available within an R package. Finally, the impacts of the EWMA smoothing constant and the size of the preliminary sample on the control chart design and its performance are studied.

中文翻译：

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当必须估计受控方差水平时，控制指数加权移动平均 S2 控制图误报行为

在监测方差时，更容易研究在参数不确定的情况下为指数加权移动平均 (EWMA) 图表设置控制限的问题，因为只需估计一个参数。简单地忽略引起的不确定性通常会导致控制图具有较差的误报性能。调整无条件控制 (IC) 平均运行长度 (ARL) 会使情况变得更糟。保证具有一定概率的最小条件 IC ARL 是解决这些困难的另一种非常流行的方法。但是，它非常保守，并且更复杂，更难以沟通。我们利用要绘制在控制图上的计划点数内的误报概率。事实证明，与控制无条件 IC ARL 相比，调整此概率会产生明显不同的限制调整。然后，我们开发了数值算法，以根据正态分布数据的样本方差来确定上下 EWMA 图表的相应修改。这些算法可在一个R包。最后，研究了 EWMA 平滑常数和初步样本的大小对控制图设计及其性能的影响。