Iqbal Javed, Noor-Ul-Amin Muhammad, Khan Imad, AlQahtani Salman A, Yasmeen Uzma, Ahmad Bakhtyar
COMSATS University Islamabad, Lahore Campus, Islamabad, Pakistan.
Abdul Wali Khan University Mardan, Mardan, Pakistan.
Sci Rep. 2023 Dec 1;13(1):21224. doi: 10.1038/s41598-023-48532-4.
In this article, we introduce a novel Bayesian Max-EWMA control chart under various loss functions to concurrently monitor the mean and variance of a normally distributed process. The Bayesian Max-EWMA control chart exhibit strong overall performance in detecting shifts in both mean and dispersion across various magnitudes. To evaluate the performance of the proposed control chart, we employ Monte Carlo simulation methods to compute their run length characteristics. We conduct an extensive comparative analysis, contrasting the run length performance of our proposed charts with that of existing ones. Our findings highlight the heightened sensitivity of Bayesian Max-EWMA control chart to shifts of diverse magnitudes. Finally, to illustrate the efficacy of our Bayesian Max-EWMA control chart using various loss functions, we present a practical case study involving the hard-bake process in semiconductor manufacturing. Our results underscore the superior performance of the Bayesian Max-EWMA control chart in detecting out-of-control signals.
在本文中，我们引入了一种新颖的贝叶斯最大指数加权移动平均（Max-EWMA）控制图，该控制图在各种损失函数下，可同时监测正态分布过程的均值和方差。贝叶斯最大指数加权移动平均控制图在检测不同幅度的均值和离散度变化方面表现出强大的整体性能。为了评估所提出控制图的性能，我们采用蒙特卡罗模拟方法来计算其运行长度特性。我们进行了广泛的比较分析，将我们提出的控制图的运行长度性能与现有控制图的性能进行对比。我们的研究结果突出了贝叶斯最大指数加权移动平均控制图对不同幅度变化的更高敏感性。最后，为了说明使用各种损失函数的贝叶斯最大指数加权移动平均控制图的有效性，我们给出了一个涉及半导体制造中硬烘焙工艺的实际案例研究。我们的结果强调了贝叶斯最大指数加权移动平均控制图在检测失控信号方面的卓越性能。
