Empirical Bayes Estimators of Reliability for Lognormal Failure Model

Empirical Bayes (EB) procedures are considered for estimating the reliability R(t;γ,σ) = gaufc[(ln t -γ)/σ] for the lognormal failure model. EB estimators are obtained for the 2 cases: i)γ is unknown and σ is known, and both γ and σ are unknown. The empirical Cdf of the maximum likelihood estimators of the parameters is used to obtain the EB estimators. ii) A smooth EB estimator of R(t;γ,σ) is developed when γ is unknown and σ is known. A modification of this estimator is proposed for both γ and σ unknown. In both cases, EB estimators are obtained for complete samples at each testing stage. Monte Carlo simulations are presented to compare the EB estimators and the maximum likelihood (ML) estimators of R(t;γ,σ). The simulations indicate that the smooth EB estimators have smaller mean squared errors than the other EB estimators or the ML estimators.