An age replacement policy via the Bayesian method
Abstract
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 nonrepairable 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 longrun average cost per unit time is minimised. We also assume that some catastrophic failures can be repaired. On the spectrum of longrun 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.
 Publication:

International Journal of Systems Science
 Pub Date:
 March 2011
 DOI:
 10.1080/00207720903576480
 Bibcode:
 2011IJSyS..42..469S
 Keywords:

 age replacement policy;
 Bayesian method;
 repairable catastrophic failure;
 the Jeffreys prior;
 conjugate prior