This article aims to estimate the probability of item replacement on an age replacement policy. An item is replaced until time T, or until a first non-repairable catastrophic failure occurs - whichever comes first. Because the sample size is relatively small under the replacement policy, we use a Bayesian approach to estimate probability. A prior choice is undoubtedly closely related to the problem under consideration. Here, we consider the (Jeffreys (1961), Theory of Probability, Oxford: Clarendon Press) prior and the conjugate prior that are justified to some extent. We also derive some approximations of the posterior and discuss certain special cases. Our objective is to determine an optimal replacement policy in which the long-run average cost per unit time is minimised. We also assume that some catastrophic failures can be repaired. On the spectrum of long-run average costs per unit time, our cost is smaller than others. Here, we use numerical examples to illustrate some known models, and make some comparisons as well.