On The Performance of a Two-Sided Shewhart Chart for Continuous Proportions with Estimated Parameters

During the recent years there was an increased interest in studying the performance of different types of control charts, under various distributional models for continuous proportions, such as percentages and rates. In this work we consider the Kumaraswamy distribution, a popular and flexible distributional model for data in the unit interval (0,1) and investigate further the properties of a two-sided chart for individual observations for monitoring these types of processes, when the process parameters are unknown. Specifically, using Monte Carlo simulation, we evaluate the performance of the chart under a conditional perspective and provide empirical rules on how to select the appropriate size for the Phase I sample. In addition, we explore possible adjustments on the control limits of the chart, which take into account the available Phase I sample. The performance of the chart is also investigated for several out-of-control situations. The results show that for small and moderate size Phase I samples, practitioners have to choose whether they prefer a guaranteed in-control performance or an improved out-of-control performance. The implementation of the considered methods in practice is discussed via two numerical examples.