I wouldn't do 3 sets to Failure 3x a week. That's a little excessive...unless you have some good genetics and aren't doing much else.
I got my girlfriend from 2-3 to a dozen basically doing a couple things which I would recommend.
Pick 2 days out of your workout week. If your M/T/TH/F, pick say M and TH.
M - pullups 3 sets x failure - 2 (aka leave a couple reps in you each set)
TH - chinups 3 x F-2 (same thing)
Do that a month or so and I can pretty much guarantee gains. I would test before you start, max chins and max pulls. Then after a month, maybe with a rest week too, test again your max.
I'm assuming you can do a handful or so right now. If you can't do any or can do 20 I would change the recommendation. Also, lose any fat you are carrying. This will make them easier. See how many you can do with a 10lb weight hanging from you to see the difference that makes.
Hope this helps.