Prior distributions in two-stage Bayesian estimation of failure rates

When operating experiences of similar but not identical systems have to be used for the estimation of failure rates, several authors suggest a two-stage Bayesian estimation. Some suggested noninformative priors for the hyperparameters lead to improper hyperposteriors which require truncation. The corresponding posteriors for the failure rates converge with increasing integration bounds to a common incidence model. This paper examines the reasons of this behavior and derives criteria for hyperpriors which lead to proper hyperposteriors. It is shown that the results achieved with the "new" prior are close to the results with the "old" prior with reasonable integration bounds.