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 S ≤ x < T 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.