Failure (or hazard) rate

Failure rate, also called hazard rate, is the instantaneous conditional rate at which survivors in a non-repairable population fail at time t. It is written h(t) and defined as f(t)/(1-F(t)) or f(t)/R(t). The document also defines average failure rate over an interval using H(t) and R(t).

Source checked6/6 values · 2026-10-25Metric

Specification

1 source

Kind	metric

Formula

h(t) = f(t) / (1 - F(t)) = f(t) / R(t)

Symbol	Name
h(t)	failure rate or hazard rate
f(t)	f(t)
F(t)	F(t)
R(t)	R(t)

Study notes

The failure rate is defined for non-repairable populations as the instantaneous rate of failure for the survivors to time t.
h(t) is the instantaneous conditional failure rate.
H(t) = ∫_0^t h(t) dt.
H(t) = -ln R(t).
F(t) = 1 - exp[-∫_0^t h(t) dt] = 1 - e^{-H(t)}.
h(t) = -d ln R(t) / dt.
Average failure rate: AFR(T1,T2) = (H(T2)-H(T1))/(T2-T1) = (ln R(T1)-ln R(T2))/(T2-T1).
AFR(0,T) = AFR(T) = H(T)/T = -ln R(T)/T.