Hello Amrendra

Depends on what type of control chart you choose. If you're considering at least an X-bar and R or X-bar and S chart (continuous data) with a sample of size of 5 or more, then the "underlying distribution" of the process your sampling from whether "normal" or "non-normal" doesn't affect the distribution of X-bars. Distribution of X-bars could be modeled by the normal curve. For this situation the standard control limit calculation procedures would be fine.

If you're considering an Individuals chart or X and Moving Range, then the control limits could be based upon the best fit mathematical curve that represents the process you're sampling from. My first question would be, is the reason that your skewed distribution doesn't follow any skewed distribution because your historical data is from a process that has both common and 'special' causes present? - i.e. really isn't a single distribution/population. If it truly is one distribution, then use software that can generate a reasonably close fit mathematical curve and set the control limits based on 95.45% (+/- 2 sigma) area under the curve rather than 99.73% (+/- 3 sigma). The reason is that with only a sample size of 1 and control limits based on (+/- 3 sigma), the beta error would be too high (85%) for a significant shift of 2 sigma if there truly was a special cause present. However the choice is yours, it depends on how critical it is to detect a special cause present.

Regards

Bruce Graham