The failure or hazard rate of a component is given by (life is in hours):
$h(t)= \begin{cases}0.015, & t \leq 200 \\ 0.025, & t>200\end{cases}$
Thus, the hazard rate is piecewise constant.
Find an expression for the reliability function of the component

Question

The failure or hazard rate of a component is given by (life is in hours):

[latex]h(t)= \begin{cases}0.015, & t \leq 200 \ 0.025, & t>200\end{cases}[/latex]

Thus, the hazard rate is piecewise constant.
Find an expression for the reliability function of the component

Accepted Answer

Using Equation 2.18 or Equation 2.33, we have

[latex]R(t)=\exp \left[-\int_0^t h( au) d au ight][/latex]

[latex]R(t)=\exp \left(-\int_{ au=0}^t h( au) d au ight)=\exp (-H(t))[/latex] (2.33)

[latex]R(t)=e^{-\int_0^t h( au) d au}[/latex] (2.18)

For

[latex]0 \leq t \leq 200: R(t)=\exp \left[-\int_0^t 0.015 d au ight]=\exp [-0.015 t] [/latex].

For

[latex]\left.t>200: R(t)=\exp \left[-\left(\int_0^{200} 0.015 d au+\int_{200}^t 0.025 d au ight] ight) ight][/latex]

[latex]\=[-(0.015(200)+0.025 t-0.025(200))][/latex]

[latex]\=\exp [-(0.025 t-2)]=\exp [2-0.025 t][/latex].

Question 2.4: The failure or hazard rate of a component is given by (life ......