Zaagan Abdullah A, Noor-Ul-Amin Muhammad, Khan Imad, Iqbal Javed, Hussain Saddam
Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan, 45142, Kingdom of Saudi Arabia.
COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan.
Sci Rep. 2024 Apr 30;14(1):9948. doi: 10.1038/s41598-024-60625-2.
This article introduces an adaptive approach within the Bayesian Max-EWMA control chart framework. Various Bayesian loss functions were used to jointly monitor process deviations from the mean and variance of normally distributed processes. Our study proposes the mechanism of using a function-based adaptive method that picks self-adjusting weights incorporated in Bayesian Max-EWMA for the estimation of mean and variance. This adaptive mechanism significantly enhances the effectiveness and sensitivity of the Max-EWMA chart in detecting process shifts in both the mean and dispersion. The Monte Carlo simulation technique was used to calculate the run-length profiles of different combinations. A comparative performance analysis with an existing chart demonstrates its effectiveness. A practical example from the hard-bake process in semiconductor manufacturing is presented for practical context and illustration of the chart settings and performance. The empirical results showcase the superior performance of the Adaptive Bayesian Max-EWMA control chart in identifying out-of-control signals. The chart's ability to jointly monitor the mean and variance of a process, its adaptive nature, and its Bayesian framework make it a useful and effective control chart.
本文介绍了贝叶斯最大指数加权移动平均（Max-EWMA）控制图框架内的一种自适应方法。使用了各种贝叶斯损失函数来联合监测正态分布过程的均值和方差的过程偏差。我们的研究提出了一种基于函数的自适应方法机制，该方法选择纳入贝叶斯Max-EWMA的自调整权重来估计均值和方差。这种自适应机制显著提高了Max-EWMA控制图在检测均值和离散度方面过程偏移的有效性和灵敏度。使用蒙特卡罗模拟技术来计算不同组合的运行长度分布。与现有控制图的比较性能分析证明了其有效性。给出了半导体制造中硬烘焙过程的一个实际例子，以提供实际背景并说明控制图的设置和性能。实证结果展示了自适应贝叶斯Max-EWMA控制图在识别失控信号方面的卓越性能。该控制图联合监测过程均值和方差的能力、其自适应特性以及贝叶斯框架使其成为一种有用且有效的控制图。
