Re: Mathematically
" equipment manufacturers publish a MTBF "
They do and then you divide them with each other and get the actual MTBF. Or, actually calculate probability of not breaking in 1 year for each component, deduce that from one and multiply them.
If you're lucky, you get something very close to 1. Typically you don't, but it doesn't matter as these things are designed so that 1% to 5% break in first year anyway.
Also, manufacturers give absurd MTBF -numbers, so it's all fantasy from the start anyway.