Long story short, I need to know if there is a formula for determining projected tolerance given X, Y, Z deviation, hole size and length of projection. If there isn't, someone in my shop is making up numbers...
It is just a matter of geometry. Determine the position of the center of the hole at top and bottom. Calculate the tilt angle of the hole centerline based on the differences in hole center position. Project that tilt angle to the specified distance and evaluate against the tolerance.
Take a look at ASME Y14.5M-1994 appendix B, or equivalent.
Simplistically, the 'projected' value is the thickness of the matting part/length of stud. The hole size is based on the size of what's going through/in the hole and the location tolerance of both.