A space shuttle has two booster rockets. Each booster rocket consists of four se

Question

A space shuttle has two booster rockets. Each booster rocket consists of four segments. The joint between adjoining segments is sealed by a pair of O-rings. The joint is properly (safely) sealed if at least one of the two O-rings works. Let Ai be the event that the ith joint is properly sealed, i = 1, . . . , 6. The system fails if at least one of the joints is not properly sealed. If the 12 O-rings fail independently of each other, each with failure probability p = 0.1, what is the probability of system failure?

Explanation / Answer

There are 12 O rings in total.

i.e., 6 pairs, each pair is in redundant mode.

So,

Failure probability of 1 pair = 0.12 = 0.01

So, Reliability of 1 pair = 1 - 0.01 = 0.99

Since there 6 pairs,

Reliability of the system = 0.996 = 0.9415

Probability of system failure = 1 - 0.9415 = 0.0585

So, answer to question asked:

0.0585

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