The Vote
This is the oldest trick. Build three of the part, feed them the same question, and take the majority answer. If each part is right with probability p, the vote is right when at least two agree: 3p² − 2p³. Then you can do it again and vote on the votes.
Below, every green square is a component giving the right answer this instant and every red one is wrong. Circles are voters, and the lamp at the top is the only thing the outside world ever sees.
Try this
- Start at 0.80 reliability and add layers. The system error shrinks by roughly an order of magnitude each time, even though each part is still wrong one time in five.
- Drop reliability below 0.50. Voting now makes things worse, because the majority is wrong and gets more confident with every layer. The cobweb shows why: 0.5 is an unstable fixed point, and repeated voting pushes toward 0 or 1.
- Put reliability back up to 0.95, use 4 layers, and nudge common-mode faults to 0.02. Your 81-part system is now only as good as the thing all 81 share.
The deep cut
The math assumes failures are independent. On 4 June 1996, Ariane 5 flew with two inertial reference units for redundancy. Both ran the same software, so both hit the same 64-bit-to-16-bit overflow within milliseconds of each other and shut down. The rocket destroyed itself about 37 seconds after launch. The spare was a copy of the same mistake.
That's why serious redundancy uses dissimilar redundancy: different chips, different teams, different languages. Airbus flight-control computers pair units built on different processors with separately written software, so a single bug can't take out every copy.