An integral-equation technique is used to evaluate the expected cost of maintaining a system functioning over the period (0,t] using two minimal-repair replacement policies. These cost functions provide appropriate criteria to determine T*, the optimal scheduled replacement period over this finite time horizon. For both policies, it is shown that significant cost savings can be achieved by using the T* values predicted by the new models with a finite time horizon rather than those obtained from the established asymptotic formulations. An adaptive finite minimal-repair replacement policy is also formulated using dynamic programming, and the expected cost of this policy is shown to be only slightly less than that of the best stationary policy.
