Asked by Gwyneth Paulino on May 01, 2024
Verified
A two-component process has an 81% success rate in series and a 99% success rate in parallel. If each component has the same reliability, what is the reliability of an individual component?
A) 50%
B) 90%
C) 99%
D) 59%
E) unable to determine
Two-Component Process
A process consisting of two distinct parts or stages that together complete a task or produce a product.
Success Rate
The percentage of attempts or operations that are successful, often used as a measure of efficiency or effectiveness.
- Acquire knowledge on the concept and determination of reliability for products that incorporate components in series and parallel layouts.
Verified Answer
CR
CLAUDIA RISCOMay 02, 2024
Final Answer :
B
Explanation :
Let's assume that each component has a reliability of x.
In series, the overall success rate is given by (0.81) = x^2, since both components must be successful for the system to work.
Solving for x, we get x = sqrt(0.81) = 0.9. This means that the reliability of each component is 90%.
In parallel, the overall success rate is given by (0.99) = 1 - (1-x)^2, since at least one component must be successful for the system to work.
Solving for x using the quadratic formula, we get x = 0.99 - sqrt(1-0.99) ≈ 0.5.
However, we know that each component has the same reliability, so the answer must be the higher value of x, which is 90%. Therefore, the answer is B) 90%.
In series, the overall success rate is given by (0.81) = x^2, since both components must be successful for the system to work.
Solving for x, we get x = sqrt(0.81) = 0.9. This means that the reliability of each component is 90%.
In parallel, the overall success rate is given by (0.99) = 1 - (1-x)^2, since at least one component must be successful for the system to work.
Solving for x using the quadratic formula, we get x = 0.99 - sqrt(1-0.99) ≈ 0.5.
However, we know that each component has the same reliability, so the answer must be the higher value of x, which is 90%. Therefore, the answer is B) 90%.
Learning Objectives
- Acquire knowledge on the concept and determination of reliability for products that incorporate components in series and parallel layouts.
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