The frequentist approach-based control charts (CCs) have been widely used to monitor the performance of the process. As compare to frequentist approach, the CCs based on the Bayesian approach can be used with a small phase-I dataset. This paper aims to propose a new homogenously weighted moving average CC based on the Bayesian theory. We have used two different loss functions, symmetric loss function as squared error loss function and asymmetric loss function as linex loss function under the informative prior as conjugate prior and noninformative prior by using posterior distribution (P dist) and posterior predictive distribution (PP dist). We calculated the values of average run length and standard deviation of run length to check the performance of the proposed homogenously weighted moving average CC based on the Bayesian theory. We also compared the proposed CC with the exponentially weighted moving average CC under the Bayesian theory. The results revealed that the proposed CC is more sensitive in the detection of small/moderate shifts than the considered CC. Finally, we presented an example based on a real-life data for implementation purposes.

中文翻译：

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基于贝叶斯理论的齐次加权移动平均控制图

基于频率论方法的控制图 (CC) 已被广泛用于监控过程的性能。与频率论方法相比，基于贝叶斯方法的 CC 可以与小的阶段 I 数据集一起使用。本文旨在基于贝叶斯理论提出一种新的均匀加权移动平均CC。我们使用了两种不同的损失函数，对称损失函数作为平方误差损失函数，不对称损失函数作为线性损失函数，在信息先验作为共轭先验和非信息先验下，通过使用后验分布（P dist）和后验预测分布（PP dist） . 我们计算了平均游程长度和游程长度标准偏差的值，以检查基于贝叶斯理论提出的均匀加权移动平均 CC 的性能。我们还将提出的 CC 与贝叶斯理论下的指数加权移动平均 CC 进行了比较。结果表明，所提出的 CC 在检测小/中度偏移方面比所考虑的 CC 更敏感。最后，我们提供了一个基于现实生活数据的示例，用于实现目的。