Suppose that a process is comprised of five components, each having an 85% success rate. By how much would reliability change if the process switched from having the components in parallel to having the components in series?
A) no change
B) 100% increase
C) 55.6% increase
D) 55.6% decrease
E) 36.3% decrease

Question

Quizplus · Accepted Answer

When components are in parallel, the overall reliability is the complement of the probability that all components fail. So, the overall reliability in parallel is given by:
R_parallel = 1 - (0.15)^5
R_parallel = 0.99923

When the components are in series, the overall reliability is the product of the individual component reliabilities. So, the overall reliability in series is given by:
R_series = (0.85)^5
R_series = 0.4437

The change in reliability when switching from parallel to series is:
ΔR = R_series - R_parallel
ΔR = 0.4437 - 0.99923
ΔR = -0.55553

So, the reliability decreases by 55.6% when switching from parallel to series. 
Therefore, the answer is D.

Suppose That a Process Is Comprised of Five Components, Each