In reliability modeling, the random
variable is the time to failure of a component. The
hazard function is defined at the left as a function of the
density and cumulative distribution. The hazard function can
be viewed as the failure rate as a function of time.
For =1, the hazard function is constant, and we say that
the component has a constant failure rate. The distribution
for time to failure is the exponential distribution. This is
often the assumption used for electronic components.
For =
2, the hazard rate is increasing linearly with time. The probability
of failure in a small interval of time, given
the component has not failed previously, is growing with time.
This is the characteristic of wear out. As the component gets
older, it begins to wear out and the likelihood of failure
increases. For larger values of the hazard function increases
at a greater than linear rate, indicating accelerating wear
out.
Alternatively, for < 1,
the hazard function is decreasing with time. This models the
characteristic of infant mortality.
The component has a high failure rate during its early life
but if it survives that period, it becomes less likely to
fail.
