The failure rate or hazard rate of a component is:

$h (t) = 0.02 t^{1.7}$ , t≥0

The failure rate is in failures per year

(a) What is the reliability function of this component and what is the value of the reliability for a period of 2 years?

(b) What is the median life or $B_{50}$ life of this component?

Question

The failure rate or hazard rate of a component is:

[latex]h (t) = 0.02 t^{1.7}[/latex], t≥0

The failure rate is in failures per year

(a) What is the reliability function of this component and what is the value of the reliability for a period of 2 years?

(b) What is the median life or [latex]B_{50}[/latex] life of this component?

Accepted Answer

(a) [latex]R(t)=\exp \left[-\int_0^t h( au) d au ight]=\exp \left[-\int_0^t 0.02 au^{1.7} d au ight]=e^{-0.007407 t^{2.7}}[/latex]

[latex]R(2)=e^{-0.007407 imes 2^{2.7}}=e^{-0.048131}=0.953009 ext {. }[/latex]

(b) [latex]R\left(B_{50} ight)=0.50=e^{-0.007407(B_{50})^{2.7}}[/latex]

[latex]\ln 0.50=-0.007407\left(B_{50} ight)^{2.7}[/latex]

[latex]B_{50}=\left(\frac{-\ln 0.50}{0.007407} ight)^{1 / 2.7}=5.37[/latex] years.

Question 2.7: The failure rate or hazard rate of a component is: h(t) = 0.......