Extended opportunity-based age replacement with a one-cycle criterion

Age replacement is a well-established theoretical model for guidance on preventive replacement of technical units, with the intention to replace units before failure, in a manner that is most cost-effective. Traditionally, the cost criterion is based on assumed use of the same replacement strategy over a period of infinite length, enabling application of the renewal reward theorem to derive the units’ optimal preventive replacement age. However, in many situations the number of renewals involving exchangeable units is typically small, which undermines the use of this traditional cost criterion. As an alternative, minimal average costs per unit time over a single cycle has been proposed, and studied for several age replacement scenarios. In this paper, this work is briefly reviewed, followed by presentation of results on the use of the one-cycle criterion for extended opportunity-based age replacement. In this model, a unit is replaced correctively in case of failure or preventively upon reaching a specific age, as in the standard age replacement model. In addition, the unit is replaced preventively if opportunities occur during a period before the optimal age replacement time, for example in case production stops due to failure or preventive replacement of other units in the same production process. As such, costs of preventive replacement in the latter case are likely to be smaller than if preventive replacement of the specific unit requires a production stop, making it clear that it will be attractive to benefit from such opportunities occurring within a certain time range prior to scheduled preventive replacement. Optimality results for this model, with the one-cycle criterion, are presented and illustrated, and it is shown how limiting cases coincide with several other age replacement scenarios. Iskandar and Sandoh (An extended opportunity-based age replacement policy. RAIRO Ops Res., 2000, 34 , 145—154) studied this model with the renewal reward criterion, but they assumed that all preventive replacements would incur the same costs. A generalization of their results is presented, allowing different costs for the two preventive replacement scenarios. This enables the comparison of the optimal replacement strategies according to the one-cycle criterion and the renewal reward criterion.