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Which sentence is correct?

I performed a reliability analysis.

or

I performed an reliability analysis.

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6

Your first sentence is correct:

I performed a reliability analysis.

The choice between a and an has nothing to do with the noun. It is entirely dependent on the sound that comes after the indefinite article.

a whole hour.

a tropical island.

an honourable solider.

If the next word after the indefinite article starts with a consonant sound, the indefinite article needs to be a.

If the next word after the indefinite article starts with a vowel sound, the indefinite article needs to be an.

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    I just wanted to reiterate that it's based on whether or not the word begins with a vowel sound, not an actual vowel, as the last example in this answer demonstrates. I've seen this trip people up before, even native speakers. – Nathan K Mar 7 '16 at 21:30
  • @NathanK In some cases you'll see people choose what looks like the wrong one of a/an because an initial consonant is silent in their dialect but not yours, or vice versa. (I can't think of an example right now.) – zwol Mar 7 '16 at 21:45
  • @zwol, something I see a lot in electronics is different a/an use depending on how people speak acronyms. I prefer to say SPI as "es-pea-eye", so I use "an" before it, other people say it as "spy", so they don't. There are probably other examples with acronyms. – Austin Mar 7 '16 at 22:16
  • @Austin: There sure are, the one that comes most readily to my mind is "LED". A led or an L E D. – Meni Rosenfeld Mar 7 '16 at 22:38
  • @zwol I wasn't really referring to differences in dialect or acronyms (or they get it wrong for their own dialect). "Herb" is a good example. In BrE the 'h' is usually pronounced while it's usually silent in AmE. – Nathan K Mar 8 '16 at 13:59
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Whether or not use use "an" depends on the word that directly follows the article.

If the initial sound of that word is a vowel sound, we use "an." Otherwise, we use "a."

For your sentence, it would be

I performed a reliability test.

because "reliability" does not start with a vowel sound.

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Whether you use a or an entirely depends on the word directly after the a/an.

An analysis

A reliability analysis

An accurate reliability analysis

etc.

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