I have found myself doing the exercise in a different order:
legs
buttocks
lower abdomen
abdomen
chest
upper back (this isn't in the book, but I seem to hold a lot of tension here, and it complements the chest)
shoulders
arms (this seems to fit better here because when I tense the chest, back, and shoulders my arms move. If done here, I don't have to move them again until the exercise is over)
neck
lower face
upper face
I do a quicker version of this exercise every night as I am lying in bed before sleep. It has helped me drop off to sleep quite quickly by relaxing me.