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

Question

Quizplus · Accepted Answer

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%.

A Two-Component Process Has an 81% Success Rate in Series