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 0.160 probability of failure. Complete parts (a) through (c).

(a) Would it be unusual to observe one component fail? Yes or No

(b) Would it be unusual to observe two component fail? Yes or No

The probability that a parallel structure with 2 identical components will succeed is

(Type an integer or a decimal. Do not round.)

(c) 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

P(Failure) = 0.16

a.

No.

b.

P(both fail) =0.16*0.16 = 0.0256 =2.56%

Yes it would be rare

P(succeding) = 1- P(both fai) = 0.9744

c.

P(suceeding) >=0.9999

1- (0.16^x) >=0.9999

x = 6

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