Hazard Function
Definition
The hazard function (or hazard rate) is defined as
$$ h(x) = \frac{f(x)}{S(x)} = \frac{f(x)}{1 - F(x)}, $$where $f$ is the PDF and $S$ is the Survival Function.
Interpretation
$h(x)\,dx$ approximates the probability of failure in the interval $[x, x+dx)$ given survival up to time $x$.