Actually the depth may be nearer 12 inches than 18 inches. I was thinking it was a 6ft fence you had.
I just replaced my fence posts for a 6ft fence recently and was advised to go down over a foot, however I decided to go for 'metpost' metal supports which hammer into the soil without any digging or mixing of materials. You then hammer the post straight into the support.
see this link
http://www.metpost.co.uk/spike_2.html
I got ours from a local Focus store about �6 each. The new posts are rock solid in the ground now.