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X and MR chart

General Notes
The XmR chart (aka ImR, perhaps others) applies SPC methods to individual observations that are collected sequentially from a process.



The use of individual observations (vs. sample means and sample variance, such as with an X-bar and R chart) has several implications:
  • The impact and benefit from the central limit theorem, with n = 1 (per subgroup), is greatly reduced, and therefore there is a much stronger assumption that the data from the process is normally distributed.
  • The X chart and the mR chart are mathematically coupled, and therefore one does not always offer additional insight over the other.  The X-bar and R chart do not have this drawback because they are mathematically independent from each other.