Abstract
This paper provides the Bayes estimators of the failure rate and reliability function for a one-parameter, exponential distribution by utilizing a point guess estimate of the parameter. For deriving the Bayes estimators, the prior distributions are chosen such that they are centered at the known prior values of parameters. The validity of proposed estimators is examined with respect to their maximum likelihood estimators (MLE) and Thompson's Shrinkage estimator on the basis of Monte Carlo simulations of 1000 samples.