When designing control charts the in‐control parameters are unknown, so the control limits have to be estimated using a Phase I reference sample. To evaluate the in‐control performance of control charts in the monitoring phase (Phase II), two performance indicators are most commonly used: the average run length (ARL) or the false alarm rate (FAR). However, these quantities will vary across practitioners due to the use of different reference samples in Phase I. This variation is small only for very large amounts of Phase I data, even when the actual distribution of the data is known. In practice, we do not know the distribution of the data, and it has to be estimated, along with its parameters. This means that we have to deal with model error when parametric models are used and stochastic error because we have to estimate the parameters. With these issues in mind, choices have to be made in order to control the performance of control charts. In this paper, we discuss some results with respect to the in‐control guaranteed conditional performance of control charts with estimated parameters for parametric and nonparametric methods. We focus on Shewhart, exponentially weighted moving average (EWMA), and cumulative sum (CUSUM) control charts for monitoring the mean when parameters are estimated.

中文翻译：

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在估计参数下保证条件性能的控制图设计

在设计控制图时，控制参数是未知的，因此必须使用第一阶段参考样本来估算控制极限。要评估监视阶段（第二阶段）中控制图的控制内性能，最常用的是两个性能指标：平均运行时间（ARL）或误报率（FAR）。但是，由于在阶段I中使用了不同的参考样本，因此从业人员的数量将有所不同。即使对于已知的数据实际分布，仅对于非常大量的阶段I数据，这种变化很小。在实践中，我们不知道数据的分布，它必须连同其参数一起进行估算。这意味着使用参数模型时必须处理模型误差和随机误差，因为我们必须估计参数。考虑到这些问题，必须做出选择以控制控制图的性能。在本文中，我们讨论了有关带有参数和非参数方法估计参数的控制图的控制中保证条件性能的一些结果。我们专注于Shewhart，指数加权移动平均值（EWMA）和累积和（CUSUM）控制图，用于在估计参数时监控均值。