Shewhart control charts with estimated control limits are widely used in practice. However, the estimated control limits are often affected by phase-I estimation errors. These estimation errors arise due to variation in the practitioner’s choice of sample size as well as the presence of outlying errors in phase-I. The unnecessary variation, due to outlying errors, disturbs the control limits implying a less efficient control chart in phase-II. In this study, we propose models based on Tukey and median absolute deviation outlier detectors for detecting the errors in phase-I. These two outlier detection models are as efficient and robust as they are distribution free. Using the Monte-Carlo simulation method, we study the estimation effect via the proposed outlier detection models on the Shewhart chart in the normal as well as non-normal environments. The performance evaluation is done through studying the run length properties namely average run length and standard deviation run length. The findings of the study show that the proposed design structures are more stable in the presence of outlier detectors and require less phase-I observation to stabilize the run-length properties. Finally, we implement the findings of the current study in the semiconductor manufacturing industry, where a real dataset is extracted from a photolithography process.

中文翻译：

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Shewhart控制图中的异常值检测模型；在光刻中的应用：半导体制造业

具有估计的控制极限的Shewhart控制图在实践中被广泛使用。但是，估计的控制极限通常受I相估计误差的影响。这些估计误差的产生是由于从业者选择样本大小的变化以及在I期中存在外围误差的缘故。由于外部误差而造成的不必要变化会扰乱控制极限，这意味着II期控制图的效率降低。在这项研究中，我们提出了基于Tukey和中值绝对偏差离群值检测器的模型来检测I相中的误差。这两个离群值检测模型与无分布一样有效和强大。使用蒙特卡洛模拟方法，我们通过拟议的异常检测模型对Shewhart图表在正常和非正常环境下的估计效果进行了研究。通过研究游程长度属性（即平均游程长度和标准偏差游程长度）来完成性能评估。研究结果表明，所提出的设计结构在存在异常检测器的情况下更加稳定，并且需要较少的I期观测来稳定行程长度特性。最后，我们实现了半导体制造行业当前研究的结果，在该行业中，从光刻工艺中提取了真实的数据集。