I think it depends on a great deal of things, style (ie number of ranks and material per rank), school, and student.
I've seen schools that you get your belt based on time and money, you will be promoted if you show up and try. I've seen these schools to promoted even if our not ready. I've not been fond of these "program dojos". Granted in some cases if they follow the program they will be ready but I've seen some piss pour black belts come out of programs like this.
I also think style makes a difference and how many ranks there are. Some schools I've seen do the tip system where you stay the same rank but you change the number of tips or strips on your belt, this way you still see progress but your ranking at a different pace sometimes.
Lastly I think it's the student the more they put in, I've known schools that promote when your ready.
My school is like that, if your ready you get promoted if not, you don't...
for me I started 02/03/2009, I had previous martial arts experience and understood stances and striking so my instructor was able to focus more on the forms and the variation of the techniques compared to what I had done. I received my first degree black sash on 11/10/2011 so just shy of 3 years. I've yet to rank up again, as I'm not ready yet. I've also been working on there external system and I'm still only a 2 degree brown belt, so for the external which we don't focus as much on it's going to take me much longer. Which i'm fine with, they'll let me know when they feel I'm ready and in the mean time they keep teaching, I keep learning