the quality of being believable or worthy of trust: After all those lies, his credibility was at a low ebb.
Sometimes, credibleness.

noncredibility, noun Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
credibility (ˌkrɛdɪˈbɪlɪtɪ)
the quality of being believed or trusted

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Word Origin & History

1590s, from M.L. credibilitas, from credibilis (see credible). Credibility gap is 1966, Amer.Eng., in reference to official statements about the Vietnam War.
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
Governing today means giving acceptable signs of credibility.
Despite its reputation as the default lie detector, the polygraph has never
  received much credibility.
But so has credibility for the claim that higher truck speeds beget better fuel
Keep your credibility in check by being totally truthful about your
  accomplishments and your net results.
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