In airline applications, failure of a component can result in catastrophe. As a result, many airline components utilize something called triple modular redundancy. This means that a critical component has two backup components that may be utilized should the initial component fail. Suppose a certain critical airline component has a probability of failure of 0.041 and the system that utilizes the component is part of a triple modular redundancy. (a) What is the probability that the system does not fail? (b) Engineers decide to the probability of failure is too high for this system. Use trial and error to determine the minimum number of components that should be included in the system to result in a system that has greater than a 0.99999999 probability of not failing.

Question

Mathematics

Saniya Knapp

22 July, 05:50

In airline applications, failure of a component can result in catastrophe. As a result, many airline components utilize something called triple modular redundancy. This means that a critical component has two backup components that may be utilized should the initial component fail. Suppose a certain critical airline component has a probability of failure of 0.041 and the system that utilizes the component is part of a triple modular redundancy. (a) What is the probability that the system does not fail? (b) Engineers decide to the probability of failure is too high for this system. Use trial and error to determine the minimum number of components that should be included in the system to result in a system that has greater than a 0.99999999 probability of not failing.

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Answers (1)

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Krystal · Answer 1

1. 0.99993108.

2. 6 components.

Step-by-step explanation:

(a) Probability of 1 component failing = 0.041

So the probability of the whole system failing = 0.041^3.

Therefore the probability of not failing

= 1 - 0.041^3 = 0.99993108.

(b).

Try 5 components:

1 - 0.041^5 = 0.99999988

6:

1 - 0.041^6 = 0.9999999952.

So the answer is 6 components.