The EWMA Wilcoxon Signed-Rank Chart with Variable Sampling Interval

In this paper, we propose a nonparametric exponentially weighted moving average (EWMA) control chart with a variable sampling interval (VSI) for monitoring the median of a continuous symmetric process distribution. The proposed chart, referred to as the VSI EWMA WSR chart, is based on the Wilcoxon Signed-Rank (WSR) test. Its out-of-control statistical performance is numerically compared with that of the fixed sampling interval (FSI) EWMA WSR chart when the underlying process distributions are normal, uniform, Laplace, scaled Student’s t, and logistic. The metric used for the performance comparisons is the steady-state average time to signal, which is determined through Monte Carlo simulations. The simulation results reveal that the VSI EWMA WSR chart significantly outperforms the FSI EWMA WSR chart in detecting the median shifts of all sizes across all distributions. The practical utility of the proposed chart is demonstrated using both simulated and real datasets. Our findings underscore the efficacy of the VSI EWMA WSR chart, highlighting its value as a tool for quality control in manufacturing and other industries.