With all due respect, if the software is plotting control limits of an implausible value (for your example, count data) then that is a problem. For some data, 0 may be the appropriate LCL. There is no requirement data be normally distributed to properly use control charts (See Shewhart and Wheeler).
There are two functions (purposes) of a control chart (as defined by Shewhart):
1. Assess the consistency/stability of the within subgroup sources of variation (this is typically quantified by using a range of the within subgroup data). This is the function of the range chart. This is done first, because the second function of the control chart method is to do a comparison of the components of variation (the within sources to the between sources). Of course, a comparison would be irrational if the basis for comparison *the within subgroup variation) was inconsistent.
2. Compare the components of variation to determine where the greatest source of variation lies. This is done using the X-bar chart. The plotted data (averages) are biased to the between sources of variation (the x's that vary at the sampling frequency). These are plotted against the control limits which are a function of the within sources of variation (again, the x's that vary at the subgroup frequency).
The limits are intended to provide guidance to the user for determining consistency and evaluating leverage. They were originally derived based on empirical data with economic risks. Not properly using control charts as they were intended confuses many users. I'll add, having control limits on the X-bar chart automatically calculated by the software when the range demonstrates inconsistency (e.g., out-of-control), is inappropriate and confuses the user.
Now, this does not mean there are not a host of other graphical techniques to display data and make other decisions. I refer only to control chart method.
"All models are wrong, some are useful" G.E.P. Box
