Discussion
An operating system (OS) crashes on the average once in 30 days, that is , the Mean Time Between Failures (MTBF) = 30 days. When this happens, it takes 10 minutes to recover the OS, that is, the Mean Time To Repair (MTTR) = 10 minutes. The availability of the OS with these reliability figures is approximately :
Answer: D
The availability is approximately 99.97%.
Availability is the fraction of time the system is up:
\[ \begin{aligned} A &= \frac{MTBF}{MTBF + MTTR} \\ &= \frac{43200}{43200 + 10} \\ &= 0.99977 \approx 99.97\% \end{aligned} \]
Here 30 days = 30 × 24 × 60 = 43,200 minutes, so both times are in minutes. The other options are far too low: 96.97% would mean about 22 hours of downtime a month, not 10 minutes.
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