Distribution-free Phase II triple EWMA control chart for joint monitoring the process location and scale parameters

Distribution-free or nonparametric control charts are used for monitoring the process parameters when there is a lack of knowledge about the underlying distribution. In this paper, we investigate a single distribution-free triple exponentially weighted moving average control chart based on the Lepage statistic (referred as TL chart) for simultaneously monitoring shifts in the unknown location and scale parameters of a univariate continuous distribution. The design and implementation of the proposed chart are discussed using time-varying and steady-state control limits for the zero-state case. The run-length distribution of the TL chart is evaluated by performing Monte Carlo simulations. The performance of the proposed chart is compared to those of the existing EWMA-Lepage (EL) and DEWMA-Lepage (DL) charts. It is observed that the TL chart with a time-varying control limit is superior to its competitors, especially for small to moderate shifts in the process parameters. We also provide a real example from a manufacturing process to illustrate the application of the proposed chart.