FMEA to begin with because there is an awful lot to do . FMEA is Failure Mode Effect Analysis. Once FMEA is completed, we would know which quality failures most effect the customer. Then you start by attacking the biggest fish first. Once he is dealt with, start on #2 and so on.
EDIT Was typing while the previous post was submitted.
EDIT2. FMEA is a common tool in the auto industry. It is a standardized proceedure that measures everything from loss of life to minor inconvenience and not noticed by customer.
EDIT 3. Frame failure could result in loss of life. A sticky cabnet door is a minor inconvenience. FMEA assigns 10X the priority to example #1, no matter how many complaints are recieved on example #2. It measures Effect and not customer satisfaction. However, the end result is increased customer confidence and satisfaction.