A server crashes on the average once in 30 days, that is, the Mean Time Between Failures (MTBF) is 30 days. When this happens, it takes 12 hours to reboot it, that is, the Mean Time to Repair (MTTR) is 12 hours. The availability of server with these reliability data values is approximately :
98.3%
Availability is the fraction of time a system is operational. With mean time between failures (MTBF) and mean time to repair (MTTR), \(A = \dfrac{\text{MTBF}}{\text{MTBF} + \text{MTTR}}\).
Step 1 — Use the same unit: MTBF = 30 days = \(30 \times 24 = 720\) hours; MTTR = 12 hours.
Step 2 — \(A = \dfrac{720}{720 + 12} = \dfrac{720}{732} \approx 0.9836\).
Step 3 — As a percentage this is about 98.4%, and the closest value offered is 98.3%.
96.3% and 97.3% would need a much longer repair time (roughly 27 and 20 hours), while 99.3% would need a repair time of only about 5 hours.
98.3% option is correct.
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