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Say for an xbar-r chart I have my data set and will need to calculate the control limits via the relevant D3 and D4 constants. I believe I have to use these instead of +/- 3 standard deviations as the constants allow for the effects of sample sizes and different distribution types (if anyone could expand on that, it would be appreciated). +/-3 standard devitions for control limits could only be used if the distribution was normal?

However, in CLT if I am sampling any consistent distribution shape with say a sample of 5 parts per hour, then the mean of these samples when plotted should produce a normal distribution once there are a decent amount of means to plot. Since the distribution is normal, the empirical rule can be applied and 99.7% of data should be within +/- 3 standard deviations.

so why do xbar-r charts not use +/-3 standard deviations?

To add further confusion, when calculating Pp/Ppk we do use +/- 3 standard deviations when and compare this to the specification limits. Why use +/- standard deviations here and not in the control charts?

Thanks for any help.