Exponential EWMA control chart for the time-between-events (TBE) has been suggested to monitor high-quality processes for the early detection of process deteriorations. Although the assumed model for the TBE observations is the exponential distribution, departures from the exponential form may occur in practice. The aim of this research is to investigate the sensitivity of the exponential EWMA chart in detecting mean shifts. It is assumed that the TBE mean is known but the assumption of exponential TBE distribution is incorrect. As test cases, various Weibull and lognormal distributions of the TBE are considered while the chart is being designed under the assumption of exponential TBE distribution. Markov chain method is implemented for calculating the performance measures such as average run length, standard deviation of run length, and percentiles of the run length distribution. A wide range of chart designs are examined and it is observed that the exponential EWMA charts can be designed to be extremely robust to departures from the assumed distribution. Numerical results and practical suggestions are provided in the following. Copyright (C) 2009 John Wiley & Sons, Ltd.