Fallout shelter special training

Do note that nothing has been made official, and this is a compilation of observations/hypotheses.

Strength

• Vault:
  • Decreased timer while working in power plants
• Wastes:
  • Needed to pry open lockers and boxes.
  • May also affect damage done by guns.
  • May increase a Dwellers capacity.

Perception

• Vault:
  • Hit chance in combat
  • Decreases water production timer of the Water Treatment and Water Purification rooms
• Wastes:
  • Find stuff like abandoned buildings
  • Critical attack cross hairs expand and contract slower, making it easier to deal maximum damage (×5) with a critical attack.

Endurance

• General:
  • Health points gained on level up (does not increase hp retroactively, max out endurance to 10+7 outfit and then start leveling to get maximum health)
  • Resist radiation and damage (11 Endurance = immune to radiation)
• Vault:
  • Food and water production timers of the Nuka-Cola bottler room.

Charisma

• Vault:
  • Improved fertility. (Reduced time to get pregnant.)
  • Decreases production timer in Radio room.
• Wastes:
  • Also chance of befriending people in the wastes (Gives the xp but no damage taken)
  • Interaction with groups of slaves

Intelligence

• Vault:
  • Med-bay (Stims and Radaway) production timers
• Wastes
  • Heal/help people

UPDATE:

• Vault/Wastelands:
  • also increases Exp gain (for level and Special stat increasing), extinguishing fire

Agility

• Vault:
  • Food production timer of the Diner and Garden rooms.
  • Increases attack speed.
• Wastes:
  • Run away from unwinnable fights taking less damage

Luck

• Vault:
  • Decreases chance of rush failure.
  • Increases amount of caps earned when resources collected from a production room (also increases chance to earn those caps)
  • Increases critical bar fill up rate.
• Wastes
  • Amount of loot found outside vault

Further reading and sources:

• Reddit: /r/foshelter What does each attribute do?
• Reddit: /r/foshelter Guys, power armor doesn't give any defensive stats in the wastes. ...
• Loading screen tips from Fallout Shelter for iOS

Tip:

• I set my shelter that way, to have the medbay spread in the vault to handle fire faster.
• the difference in having 1 or 2 intelligence is that a dweller with 2 intelligence levels up in half the time
• queuing my new matured dwellers to go to school so they get intelligence 2 or 3 then endurance for max HP and after that their main stat - super efficient

UPDATE: If you want to nerd out on more specifics, I recommend Section 7 of this Fallout Shelter Efficiency Data.

Also, here someone suggests that skills above 10 continue to benefit the dweller/explorer:

• Room efficiency data thread on Reddit

The only thing which could explain it (besides a bug) is that you may missing some electricity or water. If you haven't enough electricity your food and water supply will fall down and maybe collapse. This will increase the radiation of your dwellers. In some cases they may die on this.

Otherwise, I would say it could be a bug. I've had a situation which was nearly the same. In my case electricity was too low, which leads to the situation I described above.