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 0.12

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

Would it be unusual to observe one component fail? Y/N

What is the probability that a parallel structure with 2 identical components will succeed?

(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

No, it wont be unususal to observe 1 component fail as probability of failure of a component is 0.12

P(of a parallel structure with 2 identical components will succeed) = 1 - p(both will fail) = 1-0.122 = 0.9856

C) P(success) = 0.9999

P(failure) = 1-0.9999 = 0.0001

0.12n = 0.0001

so, n = 5

No of components needed to get success greater than 0.9999 = 5

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