Solution

The correct answer is option 1.

The availability of a system is defined as the proportion of time that the system is operational, and it is calculated as:

Availability = Uptime / (Uptime + Downtime)

Where Uptime is the amount of time that the system is operational, and Downtime is the amount of time that the system is not operational.

Given that the system has 99.99% uptime and a mean-time-between-failure of 1 day, we can calculate the Downtime as:

Downtime = MTBF * (1 - Availability)

Where MTBF is the mean-time-between-failure.

So, we can calculate the downtime as:

Downtime = 1 day * (1 - 0.9999) = 0.0001 days = 8.64 seconds

To reach the availability goal, the system must repair itself within 9 seconds after a failure, this means that the system has to be repaired in less than 3.6 seconds.