The survival rankings were designed with a few things in mind. We wanted a way to statistically rank fighters against each other while minimizing some of the normal stuff that comes with normal kill/death or streak based system. Those systems encourage things like camping and zerging. We also wanted to encourage high level armored PVP by basing the system off of armored battles. Another of the goals was to minimize the possibilities for 'cheating' the system by using a well known and well studied algorithm with minimal chances of gaming.
Only users with a confident enough armored battle rating are displayed. This requires, on average, about 5 armor battles (kills or deaths) within a couple day window before you show up. Players who maintain statistical confidence will remain on the board. This requires players to continue having armor battles throughout the rev to stay on the board. Only kills using Iron, Diamond, or Bow weapons will be counted (includes any iron and diamond tool, block, armor piece, etc. held in the hand when killing). Anyone using stone, or other random implements, like fish, will not have those specific fights calculated. It'll be as if they never happened.
The survival ranking system is based off of glicko2 http://www.glicko.net/glicko/glicko2.pdf. This is the same system used by chess federations, civplayers, quakelive, guildwars2, etc. It's a statistical system which calculates a users overall rating as well as their ratings derivation (or confidence) value. Ratings change relative to the person you kill or kills you. If a higher ranked person is killed by you, your rating will go up more than if you kill a lower ranked person. Subsequently if a higher ranked person kills you, your rating will go down less than if a lower ranked person kills you. This encourages you to go after people higher ranked than you, and makes killing the same people over and over again basically useless to your rank.
The glicko2 algorithm is implemented exactly as described above with a couple of notable changes. A minimum ratings derivation value was put in place to limit immediate new comers from showing up on the board. This requires someone to get a handful of kills or deaths before they pop into the ranks. The main reason for that is to force people to stick around for a little bit and make it less possible to just pop into the top of the ranks immediately by killing a high ranked person and hiding in a corner. The other main addition is an increase in RD decay. This is a configurable number that drops your ratings derivation down per calculation cycle. This forces players to continue fighting throughout a revision else they drop off the boards. Glicko does this by default, but it does it much too slow for our use.
If you're into this sort of thing, the source code is available at https://github.com/dan1son/mcp-glicko2