Control chart for monitoring zero-or-one inflated double-bounded environmental processes

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.