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

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