[shadowsun7]

To be fair to OP, Wheeler never claims that for stable/in-control/predictable processes roughly half of the measurements will lie above the average. The only claim he makes is that 97% of all data points for a stable process (assuming the process draws from a J-curve or single-mound distribution) will fall between the limit lines.

He can't make this claim (about ~half falling above/below the average line), because one of the core arguments he makes is that XmR charts are usable even when you're not dealing with normal distributions. He argues that the intuition behind how they work is that they detect the presence of more than one probability distribution in the variation of a time series.

Some links below:

Arguments for non-normality:

https://spcpress.com/pdf/DJW220.pdf

https://www.spcpress.com/pdf/DJW354.Sep.19.The%20Normality-M...

Claim of homogeneity detection:

https://www.spcpress.com/pdf/DJW204.pdf

[kqr]

I don't have the stats-fu to back it up but I would be very surprised if someone could point to a process where XmR charts are useful, but where the mean is not within 10–20 percentiles of the median.