Age-Replacement Policies Under Age-Dependent Replacement Costs

We consider a stochastically deteriorating system with self-announcing failures that require immediate reactive replacement. For such a system, we consider an age-replacement policy (without minimal repair) under which the system is replaced at failure (reactive replacement) or at a prescribed replacement time (preventive replacement), whichever occurs first. Motivated by factors such as decreasing salvage value or increasing costs associated with obtaining spare parts, we assume that replacement costs are non-decreasing in system age. We formulate a long-run expected cost-rate minimization model with instantaneous replacements that captures this dependency, and provide conditions under which there exists a unique optimal solution. We provide analytical and numerical results that compare the cost-rate minimizing optimal replacement policy, and its performance, to those for the case in which replacement costs are assumed to be constant. Finally, we also consider non-instantaneous replacements, and compare cost-rate minimizing and availability maximizing policies.