This is one of the responses I have recieved from an other source:
"...Even with highly nonnormal data you're usually OK if you're using X-Bar R or X-Bar S charts, because the Rule of Averages takes care of the nonnormality (i.e since you're plotting averages instead of raw data, and averages are normally distributed, uou're OK). With variables charts, there's really only a problem when using Individuals charts - a nice solution to nonnormality there is to use EWMA charts instead of individuals charts. Again, since EWMA charts use averaging the points that are plotted become approximately normally distributed..."
Any comments from experts here?