The assumption of normality is commonly considered when designing X-bar control charts. However in practice sometimes the measurements of the quality attribute are not normally distributed, especially when the size of the sample is small. For the economic statistical design of X-bar control charts the assumption of non-normality is important as it has significant effect on the estimation of the chart's parameters (n,h,k). In this paper the effect of non-normality on the solution space for the economic statistical design of X-bar control charts is studied. Considering constant sampling intervals it was observed that the assumption of non-normality reduces the valid range of k. In contrast for variable sampling intervals it was observed that the non-normal assumption has a significant effect on the lower bound for h. By understanding how the solution space is restricted by the non-normality assumption more effective solving algorithms for this problem can be developed.