Suppose that a process is comprised of five components,each having a 75% success rate.By how much would reliability change if the process switched from having the components in series to having the components in parallel?
A)no change
B)100% increase
C)76.2% increase
D)76.2 % decrease
E)50% increase

Question

Quizplus · Accepted Answer

If the five components are in series, then the probability of the process succeeding is (0.75)^5 = 0.2373.

If the five components are in parallel, then the probability of the process succeeding is 1 - (0.25)^5 = 0.9937.

The reliability in the parallel case is much higher than in the series case.

The increase in reliability is (0.9937 - 0.2373)/0.2373 = 3.16 or 316%.

But since the question asks for how much the reliability has changed, we must subtract 1 from the increase percentage to get the answer: 3.16 - 1 = 2.16 or 216%, which is approximately a 76.2% increase (since 1 + 0.762 = 1.762 or 176.2%). Therefore, the answer is C.

Suppose That a Process Is Comprised of Five Components,each Having