I'm not sure about the nature of your question, with the qualifications you gave limiting types of failure...
Two things:
1. I was trained to ALWAYS plan dives using the appropriate tables, and ALWAYS keep a running log to know my residual at any point in the expedition. If you're computer takes a dump at any time, for any reason, everything reverts to paper... if your paper is blank, there are big problems in the moment AND your diving is over until you are totally washed out (24-48 hours at least). This doesn't go away while carrying two, or even three, computers. "Plan your dive, dive your plan."
2. I bought a second hand computer from a good friend, a few years back. Without going into detail, he is qualified to service gear I've never even heard of, he is one of the few people I would fully trust with my life. The battery had been replaced, by him, with the factory service kit, a few months prior... and dove many times since the service. We were working in a shallow area (less than 40ft), doing tank drills and adjusting our gear as a dive plan, when the computer cut out. I did not have a mechanical depth gauge on the equipment at that time, and did not have a backup computer on at that moment either. We were diving in an extremely controlled environment, with a hard 40ft bottom, and were working on specific aspects of our gear setup and tank configurations... but the simple failure of an o-ring would've contributed to an extremely dangerous situation if it had happened at depth.
My last resort after TWO simultaneous computer failures: A good table, a good dive plan, lift bag and finger spool (with tiny knots every 10 ft as my last resort depth gauge)... hopefully the watch isn't broken too.