The acceptance criteria for production welds are often different then that used for welder qualification.
AWS D1.1 and ASME use different criteria for welder qualification and they have different acceptance criteria listed for the type of loading the weld is subjected to (AWS) or for different piping and vessel construction (ASME).
In the case of ASME, you have to defer to the specific construction code (Section I, Section VIII, B31.1 or B31.3 to name a few) to find the appropriate acceptance criteria.
In AWS you have to look in the appropriate welding code (D1.1, D1.2, D1.5, etc.) and determine if the weld is subject to static loads, dynamic (cyclic) loads, or if they are in tubular structures.
Best regards -Al