> If you find a problem at a process gate (quality gate), then you need to fix the process

This is essentially what Team Software Process aims to do. It applies a feedback model to the development process to continuously improve predictability and quality. However, it's time consuming and for it to work, you have to capture a lot of process artifacts like time spent on a task, defects found at every stage of development on that task. They basically try to apply something similar to statistical process control to software. It works (quality definitely improves), but it can be a PITA.