论文标题
不同损失功能下的贝叶斯EWMA和Cusum控制图
Bayesian EWMA and CUSUM Control Charts Under Different Loss Functions
论文作者
论文摘要
指数加权的移动平均值（EWMA）和累积总和（CUSUM）控制图已用于配置文件监视中，以跟踪受监视过程中发生的漂移变化。我们使用不同的损失函数，先前的分布和可能性分布来构建由后和后验预测分布构建的贝叶斯ewma和贝叶斯cusum图表。进行了仿真研究，并通过平均运行长度（ARL），运行长度（SDRL）的标准偏差，信号（ATS）的平均时间（ATS）以及信号（SDTS）的标准偏差来评估图表的性能。使用选择平滑参数，失控的移位大小和分布的超参数进行灵敏度分析。基于获得的结果，我们提供了使用贝叶斯EWMA和贝叶斯控制图表的建议。
The Exponentially Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) control charts have been used in profile monitoring to track drift shifts that occur in a monitored process. We construct Bayesian EWMA and Bayesian CUSUM charts informed by posterior and posterior predictive distributions using different loss functions, prior distributions, and likelihood distributions. A simulation study is performed, and the performance of the charts are evaluated via average run length (ARL), standard deviation of the run length (SDRL), average time to signal (ATS), and standard deviation of time to signal (SDTS). A sensitivity analysis is conducted using choices for the smoothing parameter, out-of-control shift size, and hyper-parameters of the distribution. Based on obtained results, we provide recommendations for use of the Bayesian EWMA and Bayesian CUSUM control charts.
