标题： 两威布尔百分位数之比的贝叶斯图监控性能初探 显示英文标题

标题： A first look at the performances of a Bayesian chart to monitor the ratio of two Weibull percentiles

摘要： 本研究的目的是调查一种特定贝叶斯控制图的性能，该控制图用于比较两种工艺。 该图表监控与工艺相关的关键特性百分位数的比例。 此类特性的变异性通过威布尔分布建模，并采用了一种处理威布尔数据的实际贝叶斯方法。 假设两个被监控工艺的百分位数为独立随机变量。 假设两种工艺关键特性的威布尔分布具有相同且稳定的形状参数。 这在实践中通常可以观察到，因为威布尔形状参数与主要变异因素有关。 然而，如果怀疑工艺的形状参数发生变化，可以使用相关的分布来监控其稳定性。 我们首先测试了训练数据数量对图表响应性的影响。 然后测试了图表在非常有限先验信息下的鲁棒性。 为此，先验值被更改以反映从形状参数和两个被监控工艺的百分位数原始值的50%偏移。 最后，在第一阶段后，考虑了采样分布的各种偏移组合，目的是估计图表诊断失控状态的能力。 采用了基于平均运行长度的传统方法，通过蒙特卡洛模拟进行经验计算。 显示英文摘要

摘要： The aim of the present work is to investigate the performances of a specific Bayesian control chart used to compare two processes. The chart monitors the ratio of the percentiles of a key characteristic associated with the processes. The variability of such a characteristic is modeled via the Weibull distribution and a practical Bayesian approach to deal with Weibull data is adopted. The percentiles of the two monitored processes are assumed to be independent random variables. The Weibull distributions of the key characteristic of both processes are assumed to have the same and stable shape parameter. This is usually experienced in practice because the Weibull shape parameter is related to the main involved factor of variability. However, if a change of the shape parameters of the processes is suspected, the involved distributions can be used to monitor their stability. We first tested the effects of the number of the training data on the responsiveness of the chart. Then we tested the robustness of the chart in spite of very poor prior information. To this end, the prior values were changed to reflect a 50% shift in both directions from the original values of the shape parameter and the percentiles of the two monitored processes. Finally, various combinations of shifts were considered for the sampling distributions after the Phase I, with the purpose of estimating the diagnostic ability of the charts to signal an out-of-control state. The traditional approach based on the Average Run Length, empirically computed via a Monte Carlo simulation, was adopted.