A single distribution-free (nonparametric) Phase II exponentially weighted moving average (EWMA) chart based on the Cucconi statistic, referred to as the EWMA-Cucconi (EC) chart, is considered here for simultaneously monitoring shifts in the unknown location and scale parameters of a univariate continuous process. A comparison with some other existing nonparametric EWMA charts is presented in terms of the average, the standard deviation and some
percentiles of the run length distribution. Numerical results based on Monte Carlo analysis show that the EC chart provides quite a satisfactory performance. The effect of the Phase I (reference) sample size on the IC performance of the EC chart is studied in detail. The application of the EC chart is illustrated by two real data examples.