Memory charts like EWMA-S2 or CUSUM-S2 are designed to detect a particular change in the process variance efficiently. However, the charts could be inefficient to detect some other shifts. To overcome this constraint, control charts with adaptive schemes that are efficient for a wide range of shifts can be used. This work proposes new adaptive EWMA charts for the dispersion (AEWMA-S2) based on an adaptive smoothing parameter that relates its value to the potential shift of the process. A Markov chain approach is used to optimize its design. A simulation experiment shows the advantage of the proposed charts.