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# Question Help

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Question Help

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

0.190.19

probability of failure. Complete parts  (a) through  (c). (a) Would it be unusual to observe one component  fail?

No

Yes

Would it be unusual to observe two components  fail?

No

Yes

(b) 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

nothing.

(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?

nothing

(Round up to the nearest whole  number.)

Guest Apr 18, 2017
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Probability of both components failing  = 0.19^2 → 0.0361

Probability of success for n components = 1 - 0.19^n

We want 1 - 0.19^n > 0.9999

Set 1- 0.19^n = 0.9999

n*ln(0.19) = ln(1-0.9999)

n = ln(1 - 0.9999)/ln(0.19)

n = 5.546

Round up:  n = 6.  You would need 6 components in parallel.

Alan  Apr 18, 2017