Some companies believe that Quality Engineers should only be involved in developing procedures to detect Quality problesm and to issue/adminstrate Corrective Actions. In this case the QE's role is to basically accuraately report on teh Cost of Poor Quality - or more typically accuarately report on the quality problems that cost money...
Other companies belive that the role of the QE is to help/lead the organization in the problem solving and precentive actions that reduce the Cost of Poor Quality.
Some companies include the 8 Wastes as part of COPQ...
COPQ is often a large part of average unit material cost.
It is also part Mean Repair Time and Production Down Time as you asked about in a separate post.
So given your two similar posts - I must ask why are you asking about the role of the QE in relationship to these costs? Do you believe this is not your role? Do you believe it should be part of your role? is it some other reason?