"personal credibility" is correct and can be used in written English.
Example: To ensure the success of the project, it is essential to cultivate the team's personal credibility.
Although for the patient, a focus on seeing the person is underpinned by feelings of trust and personal credibility, it can lead to feelings of 'quiet despair' and professional 'vulnerability' for the clinician.
They would have no personal credibility".
Your personal credibility is your greatest asset.
It's the whole attempt to destroy your personal credibility.
His personal credibility as a moderate is key to his party's claim to govern.
The battle over the voting system became a test of Mr. Clegg's personal credibility and judgment.
And many lost all personal credibility by abuse of the MPs' expenses system.
Public opinion polls suggest that Mr. Sharon's personal credibility is shaky.
On balance, I think it will because Bush has a fair amount of personal credibility".
Just last week, Mr. Bush was hammering at Mr. Gore's personal credibility and character.
The name instantly reminds everyone of his personal credibility and commitment to the fight.
