An extended opportunity-based age replacement policy

The present study proposes an extended opportunity-based age replacement policy where opportunities occur according to a Poisson process. When the age, x of the system satisfies x < S for a prespecified value S, a corrective replacement is conducted if the objective system fails. In case x satisfies for another prespecified value T, we take an opportunity to preventively replace the system by a new one with probability p, and do not take the opportunity with probability 1-p. At the moment x reaches T, a preventive replacement is executed independently of opportunities. The long-term average cost of the proposed policy is formulated. The conditions under which optimal values for S and T exist for a prespecified value of T and S, respectively, are then clarified. Numerical examples are also presented to illustrate the theoretical underpinnings of the proposed replacement policy formulation.