Show that the failure-rate function is given by Z(t) = t1 , t> 0, if and only if the time to failure distribution is the

Show that the failure-rate function is given by Z(t) = αβtβ−1

, t> 0, if and only if the time to failure distribution is the Weibull distribution f(t) = αβtβ−1 e

−αtβ

, t> 0.