General Notes
The XmR chart (aka ImR, perhaps others) applies SPC methods to individual observations that are collected sequentially from a process.
Assumptions
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.
See Independence of Sample Mean and StdDev for a derivation of the supporting theory.
References