Summary: We study empirical Bayes estimation of reliability in a lifetime distribution having probability density
\[ f(y|\theta)= \alpha y^{\alpha\nu-1} \exp(-y^\alpha/\theta)/ [\Gamma(\nu) \theta^\nu], \]
where \(0< \theta_1<\theta<\theta_2<\infty\) for some known constants \(\theta_1\) and \(\theta_2\). An empirical Bayes estimator \(\widetilde{\varphi}_n\) is constructed and its associated asymptotic optimality is studied. It is shown that \(\widetilde{\varphi}_n\) is asymptotically optimal, and the regret of \(\widetilde{\varphi}_n\) converges to zero at a rate \(O(\ln^2n/n)\) (for \(0<\nu <1/2\) or \(\nu=1\) cases) or \(O(\ln^{2\nu+\nu^*} n/n)\) (for \(1/2\leq\nu<1\) or \(\nu>1\) and \(\nu^*= \max(1,\nu)\) cases), where \(n\) is the number of past data available when the estimation problem is considered.