A Zaagan Abdullah, Khan Imad, Ayari-Akkari Amel, Raza Aamir, Ahmad Bakhtiyar
Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, 45142, Jazan, Saudi Arabia.
Department of Statistics, Abdul Wali Khan University Mardan, Mardan, Pakistan.
Sci Rep. 2024 Apr 18;14(1):8923. doi: 10.1038/s41598-024-59680-6.
The simultaneous monitoring of both the process mean and dispersion has gained considerable attention in statistical process control, especially when the process follows the normal distribution. This paper introduces a novel Bayesian adaptive maximum exponentially weighted moving average (Max-EWMA) control chart, designed to jointly monitor the mean and dispersion of a non-normal process. This is achieved through the utilization of the inverse response function, particularly suitable for processes conforming to a Weibull distribution. To assess the effectiveness of the proposed control chart, we employed the average run length (ARL) and the standard deviation of run length (SDRL). Subsequently, we compared the performance of our proposed control chart with that of an existing Max-EWMA control chart. Our findings suggest that the proposed control chart demonstrates a higher level of sensitivity in detecting out-of-control signals. Finally, to illustrate the effectiveness of our Bayesian Max-EWMA control chart under various Loss Functions (LFs) for a Weibull process, we present a practical case study focusing on the hard-bake process in the semiconductor manufacturing industry. This case study highlights the adaptability of the chart to different scenarios. Our results provide compelling evidence of the exceptional performance of the suggested control chart in rapidly detecting out-of-control signals during the hard-bake process, thereby significantly contributing to the improvement of process monitoring and quality control.
在统计过程控制中，对过程均值和离散度的同时监测受到了广泛关注，尤其是当过程服从正态分布时。本文介绍了一种新颖的贝叶斯自适应最大指数加权移动平均（Max-EWMA）控制图，旨在联合监测非正态过程的均值和离散度。这是通过利用逆响应函数来实现的，该函数特别适用于符合威布尔分布的过程。为了评估所提出控制图的有效性，我们采用了平均运行长度（ARL）和运行长度的标准差（SDRL）。随后，我们将所提出控制图的性能与现有的Max-EWMA控制图进行了比较。我们的研究结果表明，所提出的控制图在检测失控信号方面表现出更高的灵敏度。最后，为了说明我们的贝叶斯Max-EWMA控制图在威布尔过程的各种损失函数（LFs）下的有效性，我们给出了一个实际案例研究，重点关注半导体制造行业的硬烘焙过程。该案例研究突出了该控制图对不同场景的适应性。我们的结果提供了有力证据，证明了所建议的控制图在硬烘焙过程中快速检测失控信号方面的卓越性能，从而显著有助于改进过程监测和质量控制。
