Getting product to the customer on-time and corrrectly, is a good indicator that the training and processes are functioning. The employee that spots a problem and escalates it is the employee that is making direct improvements in the Quality System. In order for any program to be successful, it must have the support of upper managment. It's up to the managers to not only support the quality program, but to carry it out to their staff. Without a question the most important person is the leader of the organization.
Top management sets priorities, goals and fosters a positive culture.
But management direction is meaningless if employees don't follow the lead to make it possible to reach the goals. So, it is all employees in their own way. The top reviews the middle, who reviews the bottom. If the top puts other priorities ahead of quality, then so will all the others. From then on, QE pushing the change gets lip service and minimal cooperation, because all the managers and supervisors listen to the one who controls their compensation.