Process or Competence?

These days I spend a lot of my time reading about process. More specifically, about "Agile" AND Cmm(I).

The context: I am in an org, managing the "QA" team (I, me and myself), and senior management is pulling in the direction of "process" ISO, and CMM(I). We are a software organization, and have been building software for over 5 years, 4 of which were without "process" and the last 1 where we dabbled in "Agile" with extremely uneven results.

Yes, we have a problem. The symptom is that our quality is not where it should be (or even close).

Here is where the disconnect begins. Senior management feels that the "Agile" process is not working and we should go back to a "more stable waterfall". In short, it is a process issue. *I* believe that no matter what the process, if there isn't a certain basic minimum competence at ALL levels of the software hierarchy, the quality of the software is doomed to failure. A competence issue.

Senior management acknowledges the competence issue, but believes that it can be resolved with training. On the other hand, I believe that training is an input that you give a smart mind get started and cannot be a replacement for lack of aptitude.

Is process a substitute for competence?