On a Control Chart for Monitoring Rates and Proportions Based on the Standard Two-sided Power Distribution

Standard two-sided power distribution

Abstract

This paper proposes a new control chart based on the two-parameter standard two-sided power distribution for monitoring rates and proportions, that is, when the quality characteristic of interest belongs to the unit interval (0,1). Control charts based on the well-known beta and Kumaraswamy distributions are usually considered to deal with this kind of data. The standard two-sided power distribution
has many similarities to the beta and Kumaraswamy distributions and a number of advantages in terms of tractability. We evaluate and compare the performance of the new control chart with the beta and Kumaraswamy control charts through Monte Carlo simulation experiments. The simulation results reveal that the control chart based on the standard two-sided power distribution outperforms the beta and Kumaraswamy control charts in terms of run length analysis. An empirical application to a real data set is considered to
illustrate the new control chart in practice, and comparisons with the two most traditional control charts for rates and proportions (beta and Kumaraswamy) are made.