Who should pay for quality issue?

In the new company, I want to ask people one question: who should pay for quality issue.
As we know, quality issue is not caused by quality department, but caused by production, design, material, etc. However, in this company, most of people, quality issue is caused by quality department, because you detect out this problem and you have to solve the problem. Faint!
In fact, the phenomenon is not only found in my company. You can see such kind of problem in many other companies.
That's why it's difficult to be a quality guy.