It only took 8 easy steps, on the 8th I was blown away!
(Must conform to marketing standards by adding a nondescript click bait title.)
Anyways:
STEP: 1 Create a single weld bead. Make sure it is tile-able
STEP 2: Add an array to this weld bead.
STEP 3: Add a curve and make the weld bead follow the curve using the modifier “Curve”
STEP 4: Make the curve fit the desired object. For this I use a combination of the “shrinkwrap” modifier and “snap to faces”. When doing this, it prevents vertices from being place in random space. When the vertices are too far from the object, it will cause glitchiness with the “Shrinkwrap” modifier.
STEP 5: Mess with the curve settings, depending on the curve, some options work better than the others. Definitely play with the Twisting option on every curve.
STEP 6: Adjust the array duplication amount to fit the curve.
STEP 7: Add a displacement modifier using a cloud generated image. This will give the weld a bit of human variation. The more displacement, the more accurate it is to my real life welds 
Play with the cloud and displacement settings to get something good. It is sensitive, but once you get it, it is amazing!
Also thank you Rombout for bringing up the displacement idea!
STEP 8: Run around the place telling every person in a 100 foot radius that you made something beautiful.
Please let me know if you have any questions!
