ITPEC FE Morning April 2018 Question 15

Which of the following is an appropriate description concerning system availability?

a)Even if the MTBF is different, the system availability is equal if the MTTR is equal.b)If the MTTR can be shortened without changing the MTBF, the system availability improves.c)If the MTTR does not change and the MTBF increases, the system availability deteriorates.d)If the sum of the MTBF and the MTTR is equal, the system availability is equal.

Explanation

Shortening the MTTR improves availability — availability is the share of time the system is up, MTBF ÷ (MTBF + MTTR).

MTBF (mean time between failures) is the average running time between failures, and MTTR (mean time to repair) the average downtime per failure. With the MTBF fixed, a smaller MTTR shrinks the denominator, so the ratio rises: MTBF 100 hours and MTTR 10 hours give 100 ÷ 110 ≈ 0.909; cutting the MTTR to 5 hours gives 100 ÷ 105 ≈ 0.952.

Answer (b)

Why not others:

•(a) — with the MTTR fixed at 5, an MTBF of 100 gives 100 ÷ 105 ≈ 0.952 but 200 gives 200 ÷ 205 ≈ 0.976; the MTBF matters
•(c) — reversed: a longer MTBF with the same MTTR means the system is up for a larger share of the time, so availability improves
•(d) — the same sum can split differently: 90 ÷ 100 = 0.9 but 50 ÷ 100 = 0.5

Key rule: Availability rises when failures are rarer (longer MTBF) or repairs faster (shorter MTTR); only the ratio of MTBF to the total counts.

System Component · AI-written, may contain errors

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