A system has 99.99% uptime and has a mean‐time‐between‐failure of 1 day. How…

Goal: Find the required mean-time-to-repair (MTTR) to achieve 99.99% availability given MTBF = 1 day.

Formula: A = MTBF / (MTBF + MTTR)

Solve for MTTR:

• MTTR = MTBF * (1 - A) / A

• Convert MTBF to seconds: 1 day = 86,400 s

• Plug in A = 0.9999 and MTBF = 86,400 s:

• MTTR = 86,400 * (1 - 0.9999) / 0.9999 = 86,400 * 0.0001 / 0.9999

• Compute numerator: 86,400 * 0.0001 = 8.64

• Divide: 8.64 / 0.9999 ≈ 8.640864... seconds

Conclusion: The required MTTR is approximately 8.64 seconds (about 9 seconds).

Note: To strictly meet 99.99% availability the MTTR must be less than or equal to 8.640864 s. Using a rounded value of 9 s yields availability ≈ 99.9896%, which is marginally below 99.99%.