LIAI
This is a big subject but for an avionic system to be fitted to a helicopter, a contractor will typically;
Conduct a Parts Control and Standardisation Programme in accordance with, say, MIL-STD-785B. Parts selection may be in accordance with DEF STAN 59-36.
Calculate Reliability predictions for the design assembly in accordance with, for example, MIL-HDBK-217F using a rotary wing environment. Basically, a component count, factored for the environment they are to be used in.
Test Reliability in accordance with MIL HDBK 781.
Conduct Environmental testing in accordance with MIL-STD-810E. Environmental Stress Screening is a pre-condition for initial acceptance. Any equipment that has unresolved ESS Faults cannot be submitted to final Acceptance Testing. What this means is that a programme may proceed through various stages with known design faults, as long as they are resolved by an agreed milestone, perhaps Critical Design Review.
What you are paying for here are things like extreme operating temperatures. The RN will typically ask for -45C. Accepting -35C may reduce the cost by lots and speed the programme. Commercially available equivalents may only be specified to -20C. Trading off is the name of the game.
There’s much more, but the real problem is that too many equipment projects end before the Installed System Performance is demonstrated. In other words, they’ll deliver an LRU with a component count of 6000 MTBF, which fails as soon as it’s plugged into a dirty aircraft power supply or takes an oil spillage.
The modelling you speak of is included in the above. A statistical upper and lower value will be calculated but, in my opinion, this is almost inconsequential compared to the installed performance, which is a far more pragmatic test of any airborne kit. In my experience, very few equipment contracts produce kit which fails to meet its spec. But it often fails miserably when system integration is attempted. This is when MTBF, no matter how good, becomes absolutely meaningless.
I'm a great fan of the Sea King, but follow the eflux trail down the port side, and you come to an air vent for the aft avionics bay. Immediately behind it (inside) is the radar Tx/Rx cooling intake fan (Mk2/5/6). Sucking eflux straight through into the magnetron, causing corona discharge and high failure rate. The Tx/Rx exceeds its reliability spec by a factor of 3, but fails regularly because its not installed in accordance with the manufacturer's recommendations. Failures due to this are discounted from the MTBF. Best example I've ever come across. (Fixed some years ago).