Run Rules $\bar{X}$ chart are often implemented for process monitoring. The process observations are usually assumed normally distributed, and the process parameters are assumed known. In fact, a very limited number of Phase I samples may only be available to the practitioners to estimate the process parameters, the control chart's properties will vary among different practitioners. Considering this variability, the performance of the Run Rules $\bar{X}$ chart with estimated parameters is investigated. To measure this variability, the standard deviation of average run length (SDARL) is used to evaluate the performance of control chart. The results show that the Run Rules $\bar{X}$ chart requires a much larger amount of Phase I data to sufficiently reduce the between-practitioners variability. Moreover, we also investigate the properties of Run Rules $\bar{X}$ chart with estimated parameters under the non-normal distributed data. Due to the limitation of the amount of Phase I data set in practice, a bootstrap method is applied to design the Run Rules $\bar{X}$ chart. Finally, an example is provided to illustrate the application of the Run Rules $\bar{X}$ chart with estimated parameters.

运行规则 $\bar{X}$图表通常用于过程监控。通常假定过程观测值为正态分布，并且假定过程参数为已知。实际上，从业人员只能获得数量非常有限的第一阶段样本来估计过程参数，控制图的属性在不同从业人员之间会有所不同。考虑到这种可变性，运行规则的性能$\bar{X}$研究带有估计参数的图表。为了测量这种可变性，使用平均行程长度的标准偏差（SDARL）来评估控制图的性能。结果表明，运行规则$\bar{X}$图表需要大量的第一阶段数据，以充分减少从业者之间的差异。此外，我们还研究了运行规则的属性$\bar{X}$非正态分布数据下带有估计参数的统计图。由于实际上限制了阶段I数据集的数量，因此应用了一种引导方法来设计运行规则$\bar{X}$图表。最后，提供一个示例来说明运行规则的应用$\bar{X}$ 带有估计参数的图表。