AZ has the worst alts in the world, bar none.
If you don't change the battery at the same time, you can get trapped in a vicious cycle. A weak batter can over-stress an alternator, and a weak alternator can weaken a batter. You go round and round if you don't replace them together.
Replace the battery and get an alternator from www.mralternator.com
We have several of his alts running here VERY well. Including my own. You can get them in various outputs. Mine'* a 160amp. Your stocker, and AZ alts are probably 125amp, possibly 105.
Please put your year and trim level in your signature so it'* easier to answer your posts. We need to know what you drive, and what modifications you have.