Percentile-based design of exponentially weighted moving average charts

The run length is defined as the number of samples or subgroups taken before the control chart statistic exceeds the control limits.Because the distribution of run length is typically asymmetric and has a large variability, it may not be appropriate to use ARL (average run length) alone to design control charts and evaluate performance.In this paper, we introduce the concept of percentile (PL)-based design of control charts, and propose the procedure for PL-based design of EWMA (exponentially weighted moving average) charts.For the PL-based design of EWMA, we present a fitted function for the control chart coefficient, given specific percentile parameters.Additionally, we perform simulations to compare the proposed design with the ARL-based design.The simulation results show that the proposed design yields improvements in monitoring in-control processes while maintaining the ability to detect out-of-control performance.