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 .14 probability of failure.

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

Would it be unusual to observe two components fail? Yes or 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

How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9999?

Explanation / Answer

One component failing probabilty is 2*0.14*0.86 = 0.2408

Two component failing probability = 0.14*0.14 = 0.0196, which is quite low

Prob of parallel structure failing is when both components fail = 0.0196

So, probability of success = 1-0.0196 = 0.9804

say there ane n components in parallel

Prob of failure = 0.14^n

Prob of success = 1-0.14^n > 0.9999

0.14^n < 0.0001

n log0.14 > log0.0001

n>4.68 ,n =5

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