Morphological texture classification employs moments of the granulometric pattern spectrum. Classification depends on the statistical distributions of the grain size and shape. Recent work has shown the power of using asymptotic expressions for the granulometric moments which leads to successful classification in terms of an underlying random image process. These methods depend, however, on the validity of the statistical model: robustness concerns the measure of how the results are affected by various departures from the assumed model. The model may specify a normal size distribution when in fact the grain sizes are Gamma distributed; it may specify the correct type of distribution but the wrong values of its parameters; it may specify that grains are non-overlapping when in fact some are overlapping. Investigations of the robustness of the pattern spectrum mean are presented under the indicated departures from the ideal model.