$$h(t)=\lim_{\Delta t \to 0} \frac{Pr(t < T \le t+\Delta t|T \ge t)}{\Delta t}$$
Alternate names for the hazard function
The hazard rate function
The failure rate function
Force of mortality (common in actuarial science)
The bathtub-shaped hazard curve (Figure 2.2) is often used to described the lifetimes of systems or people
Infant Mortality: Systems (people) can have a relatively high probability of failure in early life
Useful Life: Systems (people) that survive the early stages of life typically experience a long period in which the probability of failure is relatively low
Wearout: As systems (people) age the probability of failure begins to increase
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