Call me crazy, but if I'm trained to complete Process A and Process A has no outputs with quality issues, customer complaints, process infractions, etc., (at least while I'm on doing Process A) have I not essentially demonstrated that I am competent?
And since we track quality issues, customer complaints, process infractions (e.g., downtime), there are your measures.
Demonstrating competence should not be a difficult or onerous activity...you're probably already doing it, but just haven't taken a step back to look at the issue from a higher perspective.