Khan Imad, Noor-Ul-Amin Muhammad, Khan Dost Muhammad, Ismail Emad A A, Sumelka Wojciech
Department of Statistics, Abdul Wali Khan University Mardan, Mardan, Pakistan.
COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan.
Sci Rep. 2023 Oct 25;13(1):18240. doi: 10.1038/s41598-023-45553-x.
Control charts, including exponentially moving average (EWMA) , are valuable for efficiently detecting small to moderate shifts. This study introduces a Bayesian EWMA control chart that employs ranked set sampling (RSS) with known prior information and two distinct loss functions (LFs), the Square Error Loss function (SELF) and the Linex Loss function (LLF), for posterior and posterior predictive distributions. The chart's performance is assessed using average run length (ARL) and standard deviation of run length (SDRL) profiles, and it is compared to the Bayesian EWMA control chart based on simple random sampling (SRS). The results indicate that the proposed control chart detects small to moderate shifts more effectively. The application in semiconductor manufacturing provides concrete evidence that the Bayesian EWMA control chart, when implemented with RSS schemes, demonstrates a higher degree of sensitivity in detecting deviations from normal process behavior. Comparison to the Bayesian EWMA control chart using SRS, it exhibits a superior ability to identify and flag instances where the manufacturing process is going out of control. This heightened sensitivity is critical for promptly addressing and rectifying issues, which ultimately contributes to improved quality control in semiconductor production.
控制图，包括指数加权移动平均（EWMA）控制图，对于有效检测小到中等程度的变化很有价值。本研究引入了一种贝叶斯EWMA控制图，该控制图采用具有已知先验信息的排序集抽样（RSS）以及两种不同的损失函数（LF），即平方误差损失函数（SELF）和线性指数损失函数（LLF），用于后验和后验预测分布。使用平均运行长度（ARL）和运行长度标准差（SDRL）曲线来评估该控制图的性能，并将其与基于简单随机抽样（SRS）的贝叶斯EWMA控制图进行比较。结果表明，所提出的控制图能更有效地检测小到中等程度的变化。在半导体制造中的应用提供了具体证据，表明采用RSS方案实施的贝叶斯EWMA控制图在检测与正常过程行为的偏差时表现出更高的灵敏度。与使用SRS的贝叶斯EWMA控制图相比，它在识别和标记制造过程失控的情况方面具有更强的能力。这种更高的灵敏度对于及时解决和纠正问题至关重要，最终有助于提高半导体生产中的质量控制。
