Which statement about the relationship between hazard rate, FIT, and MTBF is true under a constant hazard assumption?

• A. MTBF equals the reciprocal of the hazard rate; MTBF = 1/λ.
• B. MTBF is always twice the MTTR.
• C. MTBF equals FIT stated in hours.
• D. MTBF is not related to hazard rate under constant hazard.

Answer: (A)

With a constant hazard rate, the time to failure follows an exponential distribution, so the mean time between failures (MTBF) is the reciprocal of the hazard rate. The hazard rate λ is the instantaneous failure rate per hour, and for an exponential model the expected time to failure is E[T] = 1/λ, which is the MTBF.

FIT (Failures In Time) is a rate expressed as failures per 10^9 hours. Therefore FIT = λ × 10^9. Substituting λ = 1/MTBF gives FIT = 10^9 / MTBF, or equivalently MTBF = 10^9 / FIT.

This is why the statement MTBF equals the reciprocal of the hazard rate is the correct relation under a constant hazard.