Phase I is crucial for the success of the overall statistical process control (SPC) and monitoring regime. Shewhart‐type charts are recommended in this phase because of their broader shift detection ability. In this paper, a Phase I Shewhart‐type $\overline{X}$ chart is considered for the balanced random effects (also called a variance components) model. The proposed methodology takes proper account of the effects of parameter estimation and uses the false alarm probability (FAP) metric to design the chart. In the sequel, the corrected (adjusted) charting constants are calculated and tabulated. The constant can be found, on demand, from an accompanying R package. Motivations and illustrations with some real data are provided. Performance of the chart is examined in terms of in‐control robustness and detection of nonhomogeneity (out‐of‐control). The proposed chart is shown to be easily adaptable to more general models, with more variance components and nested factors, and can accommodate various estimators of variance. Thus, it enables a broader Phase I process monitoring strategy, under normality, which can be applied within the ANOVA framework applicable for many DOE models. A summary and some recommendations are provided.

中文翻译：

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第一阶段过程监控：平衡单向随机效应模型的情况

第一阶段对于整个统计过程控制（SPC）和监视机制的成功至关重要。在此阶段，建议使用Shewhart型图表，因为它们具有更广泛的移位检测功能。本文为一期Shewhart型$\overline{X}$平衡随机效应（也称为方差成分）模型被视为图表。所提出的方法应适当考虑参数估计的影响，并使用错误警报概率（FAP）度量标准来设计图表。在续篇中，计算并列出了校正（调整后）的制图常数。该常数可以根据需要从随附的R包中找到。提供了一些真实数据的动机和说明。根据控制中的鲁棒性和非均匀性检测（失控）检查图表的性能。所显示的图表显示很容易适应具有更多方差分量和嵌套因子的更通用的模型，并且可以容纳各种方差估计量。因此，在正常情况下，它可以实现更广泛的第一阶段过程监控策略 可以在适用于许多DOE模型的ANOVA框架内应用。提供摘要和一些建议。