Nuclear bunkers are not meant to save people in the world of Fallout. Vaults are for experimentation, and even though Fallout Shelter gives you no built-in way to conduct experiments, creative players are still finding ways to do "research."
Sure. Lets call it that. Research!
OK, look: this post is not for the faint of heart. Doing 'experiments' on your vault populace will occasionally mean cruelty, but arguably that's exactly what makes specialised playthroughs like these interesting in the first place. If you're running out of things to do in Fallout Shelter, or have grown bored of its mobile offerings, then perhaps vault experiments are something that could rekindle your interest.
Here are the most messed up vault experiments you can do in Fallout Shelter.
One of the easiest and most straightforward experiments to conduct is the single-gender vault. Populate your entire vault with only male or female vault-dwellers, depending on your preference. Everyone else gets sent out into the wasteland either to collect resources for your vault, or to die, depending on how dark you want things to get.
Expanding with this set-up will undoubtedly be difficult. For an all-female vault, you can keep a dude or two solely for the purposes of procreation. Otherwise, these vault-dwellers do not get to interact with anyone. For an all-male vault, things are dicier, as keeping a token woman means only a single pregnancy at a time, but it is still do-able. Either way, for both of these playthroughs you'll likely resort to a combination of radio stations and lunchboxes to expand your populace. Or, you can also simply not care about expanding, and instead focus entirely on making this themed vault more interesting. For example: an all-woman vault that only wears leather armour.
Variation: a 'normal' vault where every single baby has the same father. Lots of people are doing this one. Having the dude wear a pope suit is particularly popular.
No Food or Water
Kudos to squirmunkey for developing this sort of playthrough, which happens to exploit the systems in Fallout Shelter. It goes like this: build a vault with the normal amenities, such as a power room, a recreational area, a science lab, and a medbay...but leave the diners and water treatment plants out of it. You won't be needing those. Now get your female population pregnant, and have them man the available stations. Squirmunkey continues:
There are as many men as there are pregnant women standing outside the vault waiting to come back in. When a pregnancy ends, a man comes in and immediately starts a new one. All of the rest of the dwellers spend all their time exploring the wastes. They occasionally come back to briefly partake of the stimpaks and radaways produced by the vault. Low happiness mostly prevents production, but because everyone in the vault is immortal I can rush with impunity. When children grow up, they are sent out into the waste before they can be killed by radroaches.
Since radiation and starvation cannot actually kill your pregnant dwellers, and since raiders and radroaches cannot harm kids or pregnant women, this sort of vault doesn't need food or water. It just needs a ruthless enough overseer to go through with it, though the invincible population certainly helps.
Every room is staffed only by a single person. No dweller can interact with other dwellers. This of course would make expanding difficult, but if you'd like you can hold the occasional reproduction night.
Every vault-dweller has to earn their place in the vault. Before you take in the dweller permanently, send them off into the wasteland for a set period of time. The stipulations from here can be up to you. Maybe the dweller has to survive for one hour without any weapons. Maybe they get a weapon, but no stimpaks or radaways -- and they have to make it for an hour.
If you want to make things particularly messed-up, @TRex_Trainer suggests making this an initiation rite that every young dweller has to go through once they transition into adulthood. Any young adult that survives the wasteland for a set period of time can stay.
Variation: vault where nobody gets any weapons. Dwellers have to survive attacks purely through fist-fights. Or, a vault where you don't use lunchboxes.
Little Lamplight 2
The elderly get sent out into the wasteland: your vault is composed of only younger dwellers. If you feel particularly brave, you could try sending everyone but the children out into the wasteland, too. Kids can't die, after all.
Name everyone Gary.
Maximum Efficiency Vault
Your vault exists to produce the most resources possible. In addition to placing dwellers in the most appropriate station per their stats, every time you boot the game up, you will perform one rush in every single room available to you. If you're particularly serious about it, you can keep doing rushes until the room actually succeeds. To help this playthrough out, you'll want to upgrade your rooms as much as possible, for better gain. You might also want to consider building stat-boosting rooms, so you can buff up production.
High Stats Only
Pretty straightforward. Dwellers with low stats get sent out into the wasteland, either to die or to gather resources. Your call. Remaining dwellers all use stat-boosting rooms, to improve their skills.
I only give a dweller a name if they have at least one special above 2, and the name is based on whatever ability it is. Steven has a high strength, Lucy has a high luck, Catherine a high charisma, and so on. There are no last names. Those who don't have high skills are called Worker #xx, 0-99. Only named dwellers can breed with other named dwellers, and Workers with Workers. If a worker has a child with a high special, they are still called worker because their bloodline is impure. The only way a worker can get a name is if they go into the wasteland and bring back enough items to help the community. However, their names will only begin with W, for wasteland, and still can only breed with workers, or other Wastelanders.
Wanna build a giant gym? Or an arcade that would fit right into New Vegas? Or a giant learning facility? Pick one of the specialised rooms that you unlock a few hours into Fallout Shelter, and then reconstruct your vault so that it revolves around that one specific thing.
Variation: TRex_Trainer suggests making an Enclave/Brotherhood of Steel type vault, where dwellers can only wear power armour/scribe/lab outfits, as well as only use energy weapons.
Whatever you go with, it will likely take some time to build up the resources or gear to pull any of these off -- you can't just start out with a themed vault, unfortunately.
Section all the famil[ies] into different places in the vault and they will each have th[eir] own jobs. Example; the Smiths will work the lower left energy generators, the Henry's will work the top right cafeterias. I'll try to keep track to see which family is the most effective and which family is the least effective. Whichever family was the least effective in the 24hours, I'll take a random member of their family and send them out into the wasteland without any supplies. The most effective family will get a piece of armour or a weapon.