Suppose that a process is comprised of multiple components, each having a 75% success rate. What is the change in reliability going from a series layout to a parallel layout if the process has 5 components?
A) 0%
B) 100%
C) 76.2%
D) -76.2 %
E) unable to determine

Question

Quizplus · Accepted Answer

In a series layout, the overall reliability is the product of the individual reliabilities. For 5 components each with a 75% success rate, the overall reliability is $0.75^5 = 0.2373$ or 23.73%. In a parallel layout, the system fails only if all components fail. The failure rate of each component is 25% (100% - 75%), so the failure rate of the system is $0.25^5 = 0.0009765625$ or 0.0977%. Thus, the reliability of the system in a parallel layout is 100% - 0.0977% = 99.9023%. The change in reliability from series to parallel is $99.9023\% - 23.73\% = 76.1723\%$, which rounds to 76.2%.

Suppose That a Process Is Comprised of Multiple Components, Each