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) none of the above
E) unable to determine

Question

Quizplus · Accepted Answer

Let R be the reliability of an individual component.

In a series system, the overall success rate is the product of the individual success rates:

0.81 = R × R

Solving for R, we get R = 0.9.

In a parallel system, the overall success rate is 1 minus the product of the failure rates:

0.99 = 1 - (1-R)(1-R)

Solving for R, we again get R = 0.9.

Therefore, the reliability of an individual component is 90%.

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