Heavily armed soldiers with tanks surrounded Heathrow airport last week as a result of what was described as a “credible threat” from terrorists to the security of aircraft and passengers.
Credible seems here to be used in the way that people have employed it ever since it appeared in the English language in the fourteenth century: of something that is convincing or is capable of being believed. (It came from Latin credibilis, worthy of being believed, from the verb credere, to believe.)
At least, we have to assume that the intelligence reports on which the mobilisation was based do fall into this category. I suspect, though, that the speaker had in mind a subtly different sense of the word that grew up in the Cold War years, sometime before 1960. A credible threat was one the other side would find believable, and a credible nuclear deterrent was one that was effective in keeping the other guys in line because they would believe its owners were ready and willing to use it. So, something that was credible was able to persuade people that some event would happen.
In the middle 1960s, American politicians borrowed that extended sense for credibility gap, the chasm between the true facts and what people believe them to be, especially situations in which people refuse to take official statements at their face value, a situation that is all too evident today following last weekend’s world-wide peace marches. It was only from the late 1970s onwards, though, that young people borrowed the word in a much weakened sense to make street credibility, or street cred, to mean, not that you are believable, but that you are worthy of the respect of your peers.
Despite these modern examples, it is a little formal and old-fashioned, in particular when it refers to the idea of personal trustworthiness in semi-archaic terms like credible witness.