Sampling: Design and Analysis

In his seminal book, Shewhart (1931) makes no demand on the distribution of the characteristic to be plotted on a control chart. How then can we explain the idea that normality is, if not required, at least highly desirable? I believe that it has come about through the many statistical studies of control-chart behavior. If one is to study how a control chart behaves, it is necessary to relate it to some distribution. The obvious choice is the normal distribution because of its ubiquity as a satisfactory model. This is bolstered by the existence of the Central Limit Theorem.