I've found there is a way to survive way longer in survival mode, even if it complicates a bit the management.
1st : Don't build touching rooms. Only one room per level. One on the left of the elevator, the one below on the right, then the next below on the left again, etc. This protects you from contamination of rooms when fires, radroaches and other monsters comes from the ground. It also allows an easy escape for the dwellers towards safer rooms before their life drops too much from fighting the threat, and it protects your other rooms. Plus it's the only way to avoid a high use of Health Paks.
2nd: Send as many dwellers as you can outside early on. Even if they don't collect a lot of items, they will find some that will still be useful for your dwellers when they come back.
3rd : When the dwellers return, do not collect them immediately. Even if they are heavily wounded / irradiated, as long as you don't collect from them, they are in an immortal zone where they also don't consume any food or water, thus you don't jeopardize your valut.
4th : One dweller comes in, one goes out : To keep the precarious economy of your vault running, replace one dweller that you collect from by one dweller that is in the vault working somewhere. Switch the equipments / weapons and then send them immediately out. This is necessary as long as you don't have Health packs and Radaways. Then, you can always send the same ones outside.
5th : Don't check too often on your vault because attacks comes IMMEDIATELY when you open your vault. Wait for your dwellers to recover from their sustained wounds while the app is running in the background.
6th : Keep the most powerful weapons inside of your vault. They are more than necessary to protect it from all the bad guys coming and can save you a whole room getting wiped out.
7th : Accept that you will have a lot of losses, because the UI is stupid. It's frustrating, but it happens.
8th : Call back your dwellers when you go to bed, especially the important ones.
9th : Aim for the objectives to complete to get as many Lunchboxes as possible.
10th : Grow your population as slow as possible after you hit the 20 dwellers mark, to avoid as long as possible the really nasty creatures to attack your vault.
With these rules and a lot of patience (seems like a second work sometimes), I've managed to climb my vault population to 34, having lost only 5 dwellers in the process, till the bloody thing bugged and crashed (after 2 weeks ).