第一次看贝叶斯图的性能，以监测两个威布尔分布的比率
A first look at the performances of a Bayesian chart to monitor the ratio of two Weibull percentiles
摘要：
本工作的目的是调查一个特定的贝叶斯控制图的性能，用于比较两个过程。该图表监控与流程相关的关键特性的比值。通过韦布尔分布对这种特征的变异性进行建模，并采用实用的贝叶斯方法来处理威布尔数据。假设两个被监控过程的变量是独立的随机变量。假设两个过程的关键特征的韦布尔分布具有相同且稳定的形状参数。这在实践中通常是有经验的，因为威布尔形状参数与变异性的主要相关因素有关。然而，如果怀疑过程的形状参数发生变化，则可以使用所涉及的分布来监视其稳定性。我们首先测试了训练数据的数量对图表响应性的影响。然后，我们测试了图表的鲁棒性，尽管非常差的先验信息。为此，先前的值被改变以反映在两个方向上从形状参数的原始值和两个监测过程的最大值的50%的偏移。最后，在第一阶段之后，考虑了抽样分布的各种移位组合，目的是估计图表的诊断能力，以发出失控状态的信号。采用基于平均运行长度的传统方法，通过蒙特卡罗模拟经验计算。
英文摘要：
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.
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