In a small bowl combine the paprika, brown sugar, black pepper, cumin, dry mustard, garlic powder, cayenne pepper, and celery seed. Sprinkle mixture evenly over all sides of the ribs; rub onto the surface of the meat with your fingers. Wrap well with plastic wrap and refrigerate for 6 to 24 hours.
Meanwhile, at least 1 hour before grilling, soak wood chips in enough water to cover. Drain wood chips. For a charcoal grill, arrange medium-hot coals around a drip pan. Test for medium heat above the pan. Sprinkle the drained wood chips over the coals. Place ribs, bone sides down, on the grill rack over the drip pan. Cover and grill for 1 hour adding additional charcoal as necessary.
Meanwhile, in a small bowl stir together the vinegar, yellow mustard, and salt. Brush over ribs. Grill ribs about 30 minutes more or until tender, brushing with mustard mixture every 10 minutes. Makes 4 to 6 servings.