"If the empirical limits do not approximate the theoretical limits, then the probability model is wrong." - Dr Wheeler. That is, if the control limits for an XmR Chart differ from those for a Specialty Chart (NP, P, C or U chart), then the assumptions for the probability model for the Specialty Chart are not being met and the Specialty Chart should NOT be used. In short, forget about NP, P, C or U charts for count data.
Keep it simple - Use XmR for BOTH variable and count data.
Models are Wrong - Dr Shewhart
Down the Rabbit Hole - 1st example.
This article discusses the errors and nonsense in the first example, on page 12 in the ASQ Delaware "100 years of Quality" articles.