The nuances of imperfection: "flaw" vs. "fault"

What is similar?
Both "flaw" and "fault" refer to imperfections or defects. They can be used to describe problems or deficiencies in objects, systems, or people.
What is different?
A "flaw" often implies a minor or inherent imperfection, often with a nuance of being something that is part of the nature of the subject. "Fault" can imply a larger or more blameworthy imperfection and often carries a sense of responsibility or error.
Which one is more common?

Examples of usage
Flaw- The diamond had a small flaw that was barely noticeable.
- There's a flaw in the argument that needs to be addressed.
- Her plan was almost perfect, save for a single flaw.
- The engine failure was due to a design fault.
- It was his fault that the project was delayed.
- The electrical system had a fault that caused the power outage.