SPC and Normality test

Most continuous control charts (xbar and R,s) are robust to normality.  No, the Central Limit Theorem does not really apply to the control charts.  Don Wheeler has written some nice explanations of this.

Thanks for the kind comments.  Here is a good explanation I found on the Web.
Is normality of the original distribution a requirement to use control charts?  Depending on what literature you read the answer to this question will vary.  Wheeler (1992) points out that the assumption of normally distributed data is introduced into the control chart formulas through the use of control chart constants (used to compute the control limits).  The values for these constants are computed using a normal probability distribution for the original data.  However, Wheeler (1992) states that the control chart constants do not change appreciably even when the data display a non-normal distribution.   In fact, he demonstrated that control charts work well for non-normal data through the use of simulation studies of several skewed theoretical distributions.  Therefore, the data do not have to be normally distributed before using control charts.  The normality of the data is neither a prerequisite nor a consequence of a state of statistical control (Wheeler, 1992).