For a parallel structure of identical components, the system can succeed if at l

Question

For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.17 probability of failure. Complete parts (a) through (c).Would it be unusual to observe one component fail? Yes No Would it be unusual to observe two components fail? Yes No What is the probability that a parallel structure with 2 identical components will succeed? The probability that a parallel structure with 2 identical components will succeed is Type an integer or a decimal. Do not round.) How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9999? (Round up to the nearest whole number.)

Explanation / Answer

Each component failing probability = 0.17

a) 0.17 > 0.05 so it is not unusual.

We have to observed two components fail.

= 0.17*0.17 = 0.0289 < 0.05

So it is unusul.

b) We have already find the probability tha the parallel structure with 2 identical components will succeed.

So

1 - 0.0289 = 0.9711

c) 0.17^n = 1 - 0.9999

0.17^n = 0.0001

Taking log on both sides, we get

n * log( 0.17) = log(0.0001)

n = - 4/ ( -0.76955) =5.20

We take next whole number so n = 6

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