Bayes Statistical Inference on General \xd-Shock Model with Zero-Failure Data

In this paper, we use Bayesian method to study the estimation problem of the parameters \xd_1 and \xd_2 of the \xd-shock model associated with a Poisson process with intensity \xl under zero-failure data, where the system fails when the length of an interval between two success shocks does not fall in a prespecified interval \xd_1, \xd_2. By choosing U(0,1) and a Beta distribution as the prior distribution of the parameters respectively, we obtain the Bayesian and hierarchical Bayesian estimators of threshold level \xd_1 and \xd_2.