This answer is purely complementary and does not attempt to answer the question directly.
Another option for securing a rappel is the fireman's belay. This works on single pitch climbs when someone is at the base of the cliff, or on multi-pitch routs when someone is already at the next, lower anchor.
The belayer takes a hold of both strands of the rope, while keeping in mind to give the abseiling person enough slack to smoothly feed rope through the rappel device. In case of an emergency, the belayer pulls the rope strands tight, which causes the belay device to lock up.
I use this method whenever possible, since it is much quicker than attaching and detaching a prussic. It also eliminates the difficulty of resuming a rappel after the prussic has bitten down on the rope. In case of an emergency, the person below could safely lower the person rappelling, which is not possible with a self-belayed-abseil.
These points make the firemen's belay the preferred method when helping a novice to rappel. Someone new to ropes, harnesses, and rappel devices can concentrate on the more immediate aspects (avoiding overhangs and jerky movements,) while the belayer takes care of the unexpected, and can take an active roll in lowering, if necessary.
Some people swear by never even using a prussic, and instead lowering the first person off of the anchor, and then using the fireman's belay for the second. This methodology should only be used when lowering off of one's own gear, since the weight of the climber and the friction of the rope quickly abrades fixed rappel rings.
Benefits are: It becomes impossible to rappel off of the end of the ropes when the backup knots were forgotten (just watch out for not lowering the climber off of the end of the rope,) and if it turns out that the rope is not long enough for a double-roped rappel, the climber can climb back up on top-rope, instead of having to awkwardly climb on self-belay. I have also heard that this method can be quicker than using prussics, although I don't have any data to substantiate this claim.
Drawbacks are: When rappeling the traditional way, it is possible to extend the second's belay device with a sling, which makes it possible for both climbers to set up for rappel and check each other's work. Since this is not possible when lowering a climber first, that method should be used for experts only, since a novice should never set up an abseil without having his/her work checked (no-one really should.)