If you are welding dissimilar metals, a chemical analysis is the way to determine the A number. There are other means of determining the A number listed in Article IV.
If you are writing WPSs for ASME you should have a copy of Section IX and the applicable construction code(s). The construction code may revise/alter the requirements listed in Section IX. Anyone attempting to write a WPS for ASME without the applicable sections of the B&PV code is just asking for problems.
Best regards - Al
As Al mentioned, the composition used to determine the A number can, but doesn't have to come from the actual PQR weld metal. The most common way to do it is from the filler metal manufacturer's certification. The permitted ways are all outlined in Section IX QW-404.5