What is the difference between a series system's reliability and a parallel system's reliability?

• A. Series increases reliability via multiplication; parallel increases reliability due to redundancy.
• B. Series decreases reliability by multiplication; parallel increases reliability due to redundancy.
• C. Series has no effect on reliability; parallel equals series.
• D. Series increases reliability by adding parallel paths.

Answer: (A)

In reliability terms, how components are arranged determines how the chance the system works accumulates.

In a series setup, the system works only if every component works. That makes the overall reliability the product of the individual reliabilities (assuming independent failures): R_series = R1 × R2 × ... . Since each Ri is less than or equal to 1, multiplying them tends to reduce the overall reliability as more components are added. The multiplication reflects the requirement that all parts must succeed.

In a parallel setup, there are redundant paths, so the system works if any path works. This boosts overall reliability. For two paths with reliabilities R1 and R2, the system reliability is Rs = 1 − (1 − R1)(1 − R2). If the components are identical (R), this becomes Rs = 1 − (1 − R)^2 = 2R − R^2, which is higher than the reliability of either path alone. The redundancy is what raises the odds of the system functioning.

So the statement that a series arrangement uses multiplication to determine reliability, while a parallel arrangement increases reliability due to redundancy, correctly captures the main distinction.