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 :a)96.97%b)97.97%c)99.009%d)99.97%Correct answer is option 'D'. Can you explain this answer?

Question

Answer

System crashes once in 30 days and need 10 minutes to get repaired. Either convert 30 days into minute or 10 minute into days 30 days = 30 ∗ 24 ∗ 60 minute fraction of time system is not available = (10 / (30 ∗ 24 ∗ 60 )) ∗ 100 = 0.023% Availability = 100 - 0.023 = 99.97%

So, option (D) is correct.

Answer

Given:
- Mean Time Between Failures (MTBF) = 30 days
- Mean Time To Repair (MTTR) = 10 minutes

To Find:
- Availability of the OS

Solution:

Step 1: Calculate the Reliability (R)
- Reliability (R) is the probability that a system will operate without failure over a specific period of time.
- It can be calculated using the formula R = e^(-t/MTBF), where t is the time period.
- In this case, we need to calculate the reliability of the OS over a period of 30 days.

Step 2: Calculate the Unavailability (U)
- Unavailability (U) is the probability that a system will not be operational during a specific period of time.
- It can be calculated using the formula U = 1 - R.

Step 3: Calculate the Availability (A)
- Availability (A) is the probability that a system will be operational during a specific period of time.
- It can be calculated using the formula A = 1 - U.

Now let's calculate the availability of the OS.

Step 1: Calculate the Reliability (R)
- t = 30 days
- MTBF = 30 days

R = e^(-30/30) = e^(-1) = 0.3679 (rounded to 4 decimal places)

Step 2: Calculate the Unavailability (U)
U = 1 - R = 1 - 0.3679 = 0.6321 (rounded to 4 decimal places)

Step 3: Calculate the Availability (A)
A = 1 - U = 1 - 0.6321 = 0.3679 (rounded to 4 decimal places)

Answer:
The availability of the OS with these reliability figures is approximately 99.97%.

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