Modified Method-of-Moments in Empirical Bayes Estimation

A unit is put on test for a fixed time and the number of failures is observed. The probability distribution of the number of failures is assumed to be Poisson, and the Poisson failure intensity is assumed to be a stochastic variable with gamma prior distribution. Schafer & Feduccia introduced an empirical procedure for estimating the parameters of the prior based on method of moments. We investigate the s-efficiencies of empirical Bayes estimates of Poisson failure intensity and reliability when the prior is estimated by the Schafer & Feduccia method. Mean square errors (MSEs) are compared for a range of parameters which typifies certain military equipment failure data. The empirical Bayes estimates have high s-efficiencies for sample size more than 40. A modification of the Schafer & Feduccia procedure substantially improves s-efficiencies for small sample sizes.