(Solved):       A component has reliability function \( R(t) \), which has derivative \( ...

 

 

 

A component has reliability function \( R(t) \), which has derivative \( R^{\prime}(t) \). Which of the following is a correct expression for the hazard rate function? \( -R^{\prime}(t) \) \( -R^{\prime}(t) / R(t) \) \( \mathrm{R}^{\prime}(\mathrm{t}) /[1-\mathrm{R}(\mathrm{t})] \) \( -R^{\prime}(t) /[1-R(t)] \) A component lifetime Thas a Weibull distribution with shape parameter \( \beta=2 \) characteristic life \( \eta=3 \) Which of the following is a correct expression for the hazard function? \( 0.5 \) \( e^{-(t / 3)^{2}} \) \( 0.375 t^{2} \) \( 0.22222 t^{1} \) The failure time of a particular component is a Weibull random variable with shape parameter \( \beta=3 \) characteristic life \( \eta=8 \) Detemine to 2 decimal places the mean time to failure. Use \( \Gamma(1.33)=0.8933 \)