In many practical situations, the quality characteristics of interest assume values in the range (0,1), like rates and proportions (but they are not results from Bernoulli experiments). Most control charts built for these quality characteristics rely on monitoring parameters of their probability distribution functions or on their averages after some reparameterization of their density probability function. However, for highly asymmetric distributions, the median is a more appropriate location parameter than the average. In this paper, we propose Shewhart‐type control charts for monitoring the median of observations taken from quality characteristics double bounded after reparameterization of two probability density functions: Kumaraswamy and unit Weibull. The performance of the control charts is evaluated and compared in terms of run length (RL) analysis considering three estimators for the median. Finally, we also carry out two applications to demonstrate the applicability of these control charts.

中文翻译：

---

中位控制图用于监视非对称质量特征双界

在许多实际情况下，感兴趣的质量特征采用的值在（0,1）范围内，如比率和比例（但它们不是伯努利实验的结果）。为这些质量特性构建的大多数控制图都依赖于其概率分布函数的监视参数，或者取决于对其密度概率函数进行一些重新参数化后的平均值。但是，对于高度不对称的分布，中位数是比平均值更合适的位置参数。在本文中，我们提出了Shewhart型控制图，用于监控从质量特征双重界取的观测值的中值，该质量特征是在对两个概率密度函数（Kumaraswamy和unit Weibull）重新参数化后确定的。考虑到中位数的三个估计量，根据游程长度（RL）分析来评估和比较控制图的性能。最后，我们还执行了两个应用程序来演示这些控制图的适用性。