ε-Forced adaptive policy in age replacement

We consider the problem of minimizing the long-run average cost per unit time in age replacement with an unknown failure distribution. Utilizing the idea of ε-forced choices, which may be thought of as a modification of forced choice circles given by Fox and Rolph (Adaptive policies for Markov renewal programs, Ann. Statist.50 (1973), 334–341), we construct the adaptive policy which has a non-parametrically good property and is Bayes against a Dirichlet process prior.