Will a sperm analysis be a fool proof test to see if my vasectomy from 4 years ago has failed? my vasectomy was cautorized on all ends if that helps.

Yes: The sperm count or semenalysis is the only way to be sure the vasectomy is still working. Or if your partner gets pregnant. However, the sperm count is a lots less costly than a baby.

Yes, but...: The chance of a vasectomy failure, after 4 years, after the vasectomy was found successful through semen analysis 4 years ago, is such a small chance that testing is usually not needed. Maybe only one in a couple thousand men have a failure.