The Kumaraswamy distribution is widely used for modeling rates and proportions, such as relative humidity. Motivated by one environmental application, where the variable of interest is observed on the unit-interval and inflated at one, we propose Shewhart-type control charts based on the inflated Kumaraswamy distribution. In particular, we propose a control chart for monitoring the inflated Kumaraswamy median parameter. For highly asymmetric distributions or in the presence of outliers, the median is a more appropriate location parameter than the average. We proposed control charts considering two approaches: individual observations and non-individual observations. For the non-individual observations, three estimators were considered for the median parameter: sample median, maximum likelihood estimator, and the estimator proposed by Hodges and Lehmann (Ann Math Stat 34:598–611, 1963). The control chart performance is evaluated in terms of run length analysis. The numerical results show that the proposed control chart performed well in the two considered approaches.

Kumaraswamy 分布广泛用于建模速率和比例，例如相对湿度。受一种环境应用的启发，在单位间隔上观察感兴趣的变量并将其膨胀为 1，我们提出了基于膨胀的 Kumaraswamy 分布的休哈特型控制图。特别是，我们提出了一个控制图来监控夸大的 Kumaraswamy 中值参数。对于高度不对称分布或存在异常值的情况，中位数是比平均值更合适的位置参数。我们提出了考虑两种方法的控制图：个体观察和非个体观察。对于非个体观察，中值参数考虑了三个估计量：样本中值、最大似然估计量、以及 Hodges 和 Lehmann 提出的估计量（Ann Math Stat 34:598–611, 1963）。控制图性能根据游程分析进行评估。数值结果表明，所提出的控制图在两种考虑的方法中表现良好。