I just went through the Nelson Stud catalog and they mysteriously do not quote any AWS specs except for "AWS D1.1 for physical and chemical propereties of mild steel studs".  In the back of my mind I thought there was a different AWS spec just for stud welding (using the gun, not the manual fillet weld).  As I have time, I will check AWS Codes.

Unless I'm mis-understanding your question, I believe that AWS D1.1:2008 Clause 7.7 The Pre-production testing qualifies the operator, machine, studs, and positions. If you have out of position or unapproved base materials, then you have to go through all of the testing in Clause 7.6 first and then use Clause 7.7 for each shift of stud welding after that.

Changing stud guns, brand name, or stud diameter are not considered to be important factors, however a different setting is required when there is a change in stud diameter.  For arc stud welding, the current and weld time are automatically controlled by the settings on the power supply.  The settings on the power supply are dialed in based on the stud diameter, and the results are subjected to production proof tests.  One setting that is not automatic is that when setting up the gun, the “legs” on the gun need to be adjusted in or out based on the stud length.  The stud should extend about 1/8” beyond the ferrule.  This setting affects the plunge, which in turn affects fusion to the base metal and weld quality.