I know it's not the done thing to give two answers, but so much depends on the context and you haven't really given us any. A firework that doesn't go off is most definitely a dud. However, even if the firework is e.g. a rocket or a Catherine wheel, rather than a squib, the expression 'damp squib' could also be used and would not only be absolutely acceptable, but also has the advantage of a second, metaphoric meaning.
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dud informal
n noun
1 a thing that fails to work properly.
ORIGIN
Middle English: of unknown origin.
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squib
n noun
1 a small firework that hisses before exploding.
ORIGIN
C16: of unknown origin; perhaps imitative of a small explosion.
(Both from "The Concise Oxford English Dictionary)
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squib (skwb)
n.
1.
a. A small firecracker.
b. A broken firecracker that burns but does not explode
(From: http://tinyurl.com/2uuuf8)
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[edit] Origin of the phrase "damp squib"
Being an explosive, cheaper uninsulated squibs need to be kept dry in order to ignite, so a "damp squib" is literally one that fails to ignite because it got wet. The phrase "damp squib" has since come into general use to mean anything that fails to meet expectations.[5] The word "squib" has come to take on a similar meaning even when used alone, sometimes referring to a firecracker that fails to fully explode,[6] or a bullet that fails to leave the gun barrel (similar in meaning to the word "dud").
(From: http://tinyurl.com/2vamnr)