Question

# Question: For a parallel structure of identical components, the system can succeed if at least one...

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 0.22 probability of failure. (A)Would it be unusual to observe one component fail? Would it be unusual to observe two components fail? (B)What is the probability that a parallel structure with 2 identical components will succeed? How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9999?

A. It would/would not be unusual to observe one component fail, since the probability that one component fails, ?, is greater/less than 0.05. It would/would not be unusual to observe two components fail, since the probability that two components fail, ?, is greater/less than .05

(A)

Correct option:

It would not be unusual to observe one component fail, since the probability of one component fails = 0.22 is greater than 0.05.

(B)

the probability of two components fail = 0.222 = 0.0484

Correct option:

It would be unusual to observe one component fail, since the probability of two components fail = 0.222 = 0.0484 is less than 0.05.

(c)

With n components, the probability the system will succeed is greater than 0.9999 is given by:

i.e.,

Taking logarithm on both sides, we get:

i.e.,

i.e.,

i.e.,

n < 6.0828

So,

n = 7

So,

Number of components needed in the structure = 7