Yes I simplified it, I said exactly the same thing a bit earlier on (see post below)One kind of failure is when the device is dead. Another kind is when it gives you bad numbers. 5 can work against 4 failures of the former kind; with the latter all bets are off, generally speaking. Consensus vote only works if the majority agrees on the number.
The problem is slightly different with multiple controllers wrestling over one solenoid.
However with 2 not giving a result, this increases the chances that you are in fact having 3 failures and the third one is not reliable.
The real probability of having 2 failing without the 3rd one is probably hard to estimate.
IMHO, in a real life system, the probability of the third one not failing when the two other failed is a lot lower than the probability of this unit failing alone, because the failure could be due to a leak or a bad service or something similar that could affect all units.
It’s a bit similar to what’s the probability of flipping head:
- if you got two tails previously: it’s 1/2 of course as tosses as independent
- If you got 1 000 000 tails in a row previously. Maybe you want to check if you are not being tricked with a two tailed coin, that’s possibly more probable that 1/2 to the power of 1000000
You could do this with three sensors:
3 units can guarantee only against 1 failure
- No failures: 3 sensors give the same reading
- 1 failure: 2 sensors give the same reading and you are still fine and possibly indicate the failure
- 2 failures: if the two failures give no reading you just take the only reading and report 1/3 units possibly working. If the at least one of the two failures units give a reading, you cannot give a single value
5 against 2 failures maximum ?