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 .12 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

Given that probability of failuare = 0.12

Here for unusual observation probability is less than 0.05

Would it be unusual to observe one component fail?

Probability that one component fail is 0.12 which is greator than 0.05 so the observation is usual.

So answer is no.

Would it be unusual to observe two components fail?

The probability that two components fail = 0.12*0.12 = 0.0144

This probability is less than 0.05 so the observation is unusual.

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

Here the total probability is 1 and the probability that two components fail is 0.0144

Therefore required probability = 1 - 0.0144 = 0.9856

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

Here we have to find n for given probability 0.9999.

i.e symbolically it can be written as

0.12^n = 1 - 0.9999

0.12^n = 0.0001

take ln on bothsides,

nln(0.12) = ln(0.0001)

n*-2.1203 = -9.2103

n = -9.2103 / -2.1203 = 4.344 which is approximately equal to 4

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