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Condition-based maintenance (CBM) has received increasing attention in the literature over the past years. The application of CBM in practice, however, is lagging behind. This is, at least in part, explained by the complexity of real-life systems as opposed to the stylized ones studied most often. To overcome this issue, research is focusing more and more on complex systems, with multiple components subject to various dependencies. Existing classifications of these dependencies in the literature are no longer sufficient. Therefore, we provide an extended classification scheme. Besides the types of dependencies identified in the past (economic, structural, and stochastic), we add resource dependence, where multiple components are connected through, e.g., shared spares, tools, or maintenance workers. Furthermore, we extend the existing notion of structural dependence by distinguishing between structural dependence from a technical point of view and structural dependence from a performance point of view (e.g., through a series or parallel setting). We review the advances made with respect to CBM. Our main focus is on the implications of dependencies on the structure of the optimal CBM policy. We link our review to practice by providing real-life examples, thereby stressing current gaps in the literature.

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We consider an appliance manufacturer's problem of controlling the inventory of a service part in its final phase. That phase begins when the production of the appliance containing that part is discontinued (time 0), and ends when the last service contract on that appliance expires. Thus, the planning horizon is deterministic and known. There is no setup cost for ordering. However, if a part is not ordered at time 0, its price will be higher. The objective is to minimize the total expected undiscounted costs of replenishment, inventory holding, backorder, and disposal (of unused parts at the end of the planning horizon). We propose an ordering policy consisting of an initial order-up-to level at time 0, and a subsequent series of decreasing order-up-to levels for various intervals of the planning horizon. We present a method of calculating the optimal policy, along with a numerical example and sensitivity analysis.