While researching redundancy, I stumbled across this gem: Factor of Safety Versus Redundancy - The Cliff-Hanger Question. I suggest you read it yourself and ignore my summary. This guy is good, you can actually understand him. But if not, read on.
The premise is really simple; "Imagine you were hanging off a cliff. Is it safer to be attached to 2 ropes or a single rope that is twice as strong?"
Basically there are 4 scenarios:
- Case 1: Normal boring single rope.
- Case 2: Double strength single rope.
- Case 3: Normal strength double ropes, all weight on 1 rope at a time (ie. rope A breaks and B catches instantly).
- Case 4: Normal strength double ropes, both ropes take 1/2 load.
Variables and Answers
Now then, here are the variables (not that you really need them):
- λ - Lambda. Factor of safety (capacity / load)
- P(x) - Probability of 'x' failing. Ie. P(1) is probability of case 1 failing.
- N - Minimum number of units needed for success. Ie. You need 1 rope, so N=1.
- K - Number of back-ups.
So. Math aside, here are the answers.
| Case | λ | Redundancy (N + K) |
P(x) | Comment |
|---|---|---|---|---|
| 1 | 1.5 | N + 0 | 0.0828 | Base Case |
| 2 | 3.0 | N + 0 | 0.000783 | Increase λ only |
| 3 | 1.5 | N + 1 | 0.00685 | Increase redundancy only |
| 4 | 3.0 | N + 1 | 0.000 000 613 | Increase λ and redundancy |
Now, some food for thought...Two ropes are better than one double strength rope, but if they are only through a single anchor that gives way, or the rope snaps in the middle, what do you do?