Department of Statistics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa, Pakistan.
Department of Statistics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan.
Sci Rep. 2023 Jun 10;13(1):9463. doi: 10.1038/s41598-023-36469-7.
The memory-type control charts, such as cumulative sum (CUSUM) and exponentially weighted moving average control chart, are more desirable for detecting a small or moderate shift in the production process of a location parameter. In this article, a novel Bayesian adaptive EWMA (AEWMA) control chat utilizing ranked set sampling (RSS) designs is proposed under two different loss functions, i.e., square error loss function (SELF) and linex loss function (LLF), and with informative prior distribution to monitor the mean shift of the normally distributed process. The extensive Monte Carlo simulation method is used to check the performance of the suggested Bayesian-AEWMA control chart using RSS schemes. The effectiveness of the proposed AEWMA control chart is evaluated through the average run length (ARL) and standard deviation of run length (SDRL). The results indicate that the proposed Bayesian control chart applying RSS schemes is more sensitive in detecting mean shifts than the existing Bayesian AEWAM control chart based on simple random sampling (SRS). Finally, to demonstrate the effectiveness of the proposed Bayesian-AEWMA control chart under different RSS schemes, we present a numerical example involving the hard-bake process in semiconductor fabrication. Our results show that the Bayesian-AEWMA control chart using RSS schemes outperforms the EWMA and AEWMA control charts utilizing the Bayesian approach under simple random sampling in detecting out-of-control signals.
记忆型控制图，如累积和 (CUSUM) 和指数加权移动平均控制图，更适合检测位置参数生产过程中的小或中等偏移。在本文中，提出了一种新的基于贝叶斯自适应 EWMA（AEWMA）控制图的方法，利用有序集抽样（RSS）设计，在两种不同的损失函数下，即平方误差损失函数（SELF）和线损函数（LLF），以及信息先验分布，以监测正态分布过程的均值偏移。采用广泛的蒙特卡罗模拟方法来检查基于 RSS 方案的建议贝叶斯-AEWMA 控制图的性能。通过平均运行长度（ARL）和运行长度标准差（SDRL）来评估提出的 AEWMA 控制图的有效性。结果表明，与基于简单随机抽样（SRS）的现有贝叶斯 AEWAM 控制图相比，应用 RSS 方案的建议贝叶斯控制图在检测均值偏移方面更敏感。最后，为了展示不同 RSS 方案下提出的贝叶斯-AEWMA 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过程的数值示例。结果表明，在检测失控信号方面，基于 RSS 方案的贝叶斯-AEWMA 控制图比基于简单随机抽样的贝叶斯 EWMA 和 AEWMA 控制图表现更好。
