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.

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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?\"

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Basically there are 4 scenarios:

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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.

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Variables and Answers

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Now then, here are the variables (not that you really need them):

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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.

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So. Math aside, here are the answers.

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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

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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?

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