ITPEC IP October 2020 Question 14

Which of the following is an explanation of the reliability index that is calculated by the expression below?

MTBFMTBF + MTTR

a)Average time until a system failure occursb)Average time taken to recover a system after a failurec)Proportion of the operation time of a system to the total timed)Proportion of the downtime of a system to the total time

Explanation

The proportion of operating time to total time — MTBF ÷ (MTBF + MTTR) is the availability (operating ratio) of the system.

A system alternates between running and being repaired. MTBF (mean time between failures) is the average running time from one failure to the next; MTTR (mean time to repair) is the average time taken to recover. One cycle therefore lasts MTBF + MTTR, and MTBF of it is operating time, so the expression gives the share of the total time the system is operating.

For example, with MTBF = 480 hours and MTTR = 20 hours: 480 ÷ (480 + 20) = 0.96, so the system is available 96% of the time.

Answer (c)

Why not others:

•(a) — the average time until a failure occurs is MTBF on its own, a time rather than a ratio
•(b) — the average time taken to recover after a failure is MTTR on its own
•(d) — the proportion of downtime is MTTR ÷ (MTBF + MTTR), which is 1 minus the availability

Key rule: Availability rises in two ways: fewer failures (a longer MTBF) or faster recovery (a shorter MTTR).

System Component · AI-written, may contain errors

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