Effect of non normality on statistical control charts

It is well known that X̄ and R control charts are constructed based on the assumption that the measurable quality characteristic of the process is distributed normal or approximately normal. In many situations we may have reasons to believe that the underlying distribution is far from normal. In fact many applications of quality control charts the normality assumption is applied without the knowledge of the shape of the underlying distribution of the characteristic of interest. In This paper a positively skewed distribution is used to show the effect of non-normality on the significance levels of the control charts. It is found that the sign and size of the error in significance level depends on the sample size and the nominated significance level. The solutions to the problem of validity of the normality assumption which are discussed in this paper are the use of exact distribution, the split method and the weighted variance method. Tables of control charts constants for different values of sample size for the weighted variance method are given.