Solution

Reliability

Probability of failure-free operation for specified time in specified environment.

ROCOF, MTTF, MTTR with Example

• ROCOF = Rate of Occurrence of Failures - Failures per unit time. Ex: 2 failures/year → ROCOF=2/yr, higher ROCOF = less reliable. Reciprocal of MTBF in steady state.

• MTTF = Mean Time To Failure - Average time system runs before failing (for non-repairable). Ex: 5 printers fail avg after 1000 hours → MTTF=1000h.

• MTTR = Mean Time To Repair - Avg time to repair. Ex: Avg 2 hours to fix printer → MTTR=2h.

Relations:

• MTBF = MTTF + MTTR (for repairable)
• Availability = MTTF / (MTTF+MTTR) - Ex: MTTF=1000h, MTTR=10h → Availability=1000/1010=99%
• Reliability function $R(t)=e^{-λt}$ where $λ=ROCOF$

Example: E-commerce server: MTTF=500h, MTTR=5h → MTBF=505h, Availability=99%, ROCOF≈0.002 failures/hour.