# In teachingApps: Apps for Teaching Statistics, R Programming, and Shiny App Development

### Properties of The Hazard Function $h(t)$

• The hazard function relates the instantaneous, conditional probability of failure in $t+\Delta t$ given $T>t$

$$h(t)=\lim_{\Delta t \to 0} \frac{Pr(t < T \le t+\Delta t|T \ge t)}{\Delta t}$$

• 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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teachingApps documentation built on July 1, 2020, 5:58 p.m.