Each component, solder joint, wire, ... have a probability of failing.

See it as a large number of dices with very many sides.

If you have a dice with 100,000 sides and you throw it - what is the probability of getting the value 1?
If you have 100 components, then you suddenly have 100 dices - what is the probability that any single one of the dices will show 1? Obviously - the more components (dices) the bigger probability of getting a one (failure).

Different components have different probability of failing, so basically different number of sides.

Normally all designs will get lower MTBF when you add more components.

But in some situations, you can get better - you might have redundancy, in which case a broken PSU means the twin PSU can continue to supply power.

The MTBF is very much affected by environment - you often get twice as many failures whenever you increase the temperature with 10 degrees. Lots of product testing is done in climate chambers where accellerated tests are performed by running the equipment at extended temperatures to try to guestimate (yes, it's a guess since MTBF tries to put a measure on random processes and it's even a greater guess since a manufacturer don't want to wait 10 years before releasing a product just to check how 1000 units of the product behaves during the 10 years).

Note that in real life, the failure rate may be much higher (lower MTBF) because real customers introduces additional punishment - dropping equipment, having carpets producing huge amounts of ESD etc.

But in the end, you need help from a consultant to try to compute any MTBF figures for a complete product, and you need to bring in information about solder processes, types of PCB, ...