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

Would it be unusual to observe one component fail? No : as probabilty of happening that is significant.=0.14

Would it be unusual to observe two components fail? Yes: as probabilty of that =0.14*0.14=0.0196 is very low

probabilty that parallel structure with 2 identical components will succeed =P(at least one component will work)

=1-P(both the componenets will not work) =1-(0.14)2 =0.9804

let x component be needed

hence  0.9999 >1-(0.14)x

0.0001>0.14x

taking log and solving

xln(0.14)<ln(0.0001)

x>4.68

hence number of components should be at least 5.

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