AbstractA component has time to failureXwith densityf(·). Opportunities arise as a Poisson process of rateλ. At an opportunity the component may at choice, be replaced at costc2. At failure the components can either be minimally repaired at costc1or replaced at costc4. Finally the component may be replaced at any time at an‘interrupt’cost ofc3. We derive expressions for the long-run expected cost rate, and give examples of numerical optimisation with respect to control limits on age at an opportunity, and at an interrupt replacement.