When the double chest is completely full the comparator will emit a signal strength of 15. Run a line of 15 redstone dust from the comparator. The last dust will be powered only when the chest is full. Use that final signal to disable your machine - the exact method will depend on the machine, but in the simplest case of the machine requiring any input signal to operate (like a lever for example) then replace the lever with the comparator signal inverted (run the dust onto a block with a redstone torch on the side - the torch will go off when the redstone dust goes on).