Re: fence panel formula
IMHO, you're over complicating things.
A fence, by nature, is going to expand and contract, so the space you set them at will change during seasonal and weather changes. The average fence board that you describe is 5-1/2", however, that number can fluctuate anywhere from 5-1/4" to 5-5/8", there's no telling what each board's actual dimension is going to be as you pull it from the stack. Your 3/16" spacing is going to shrink in the wet/rainy season and expand to well over 1/2" in the dry season. You're also assuming that you'll precisely place your posts so that you'll have even reveals as you go along.
I say make this as easy as possible on yourself. Set your posts at a maximum spacing of 7'6". This will allow slight variances that will occur due to roots, old post cores, etc that get in the way AND still be able to utilize an 8' rail to it's fullest. Once the posts are set, you run the rails, then start your first picket covering the post, and tightly butt the next picket to the first. Set a string line to guide the tops of the pickets to be straight.
As for ripping a set amount from a picket to make it a particular dimension, as earlier stated, the width of pickets varies greatly, so there's no way to take off "XX" amount from each and having uniform boards. What you'd have to do is run every picket through a table saw where the overall width is set by the entire board, not the part being cut and discarded, if that makes any sense. If these are dog eared or shaped pickets, then you are introducing other issues as well, from having to re-dog ear the picket to reprofiling it.
I suffer from CDO ... Its like OCD, but in alphabetical order, LIKE IT SHOULD BE!!!