## 2 Related Work  
Some studies have utilized linear programming to optimize maintenance costs, taking into consideration the RUL prediction [11; 12; 13; 14], while others employed deep reinforcement learning (DRL) for the same purpose [15; 16]. Multi-objective approaches were exploited by [17] to find solutions that represent a compromise between maintenance cost and equipment availability and by [18] to optimize maintenance costs, resource utilization, and reduce carbon footprint. The authors of [19] exploited an RUL estimation based on the visual monitoring of crack damages, while [20] used deep learning (DL) for RUL estimation, aiming to develop dynamic maintenance scheduling. Refs. [21; 22] exploited an RUL model to group assets to be repaired to minimize maintenance costs. Most predictive maintenance (PdM) approaches currently adopt maintenance planning based on a static degradation threshold [4; 23; 24; 25], which is utilized to determine the moment when an intervention should be performed. Determining the optimal threshold to minimize costs typically involves considering the RUL and an additional safety factor to account for imperfect RUL predictions [12], which often necessitates combining simulation with various optimization techniques. Preventive maintenance (PM) can be utilized without a predictive model. It is widely adopted by enterprises since it only requires data concerning the time between failures. Commonly, in practical industrial scenarios, PM is scheduled in two ways: (1) maintenance actions are scheduled at equally spaced intervals based on the mean time between failures (MTBF), determined by the component's supplier or historical data; (2) maintenance actions are programmed with a high safety factor to prevent any failures from occurring. Scheduling interventions based on the MTBF aim to strike a balance between minimizing failures and utilizing the asset's useful life. However, this approach may not be efficient in minimizing costs since it may allow several failures to occur. Furthermore, it fails to account for variations in operational conditions resulting from production changes or component degradation, which are crucial for the proper functioning of tools and equipment. For example, the degradation level of a given tool may be accelerated due to the age of the machine with which it is coupled. In this scenario, the majority of tools will fail before the MTBF calculated from historical data. Although there are proposed methods to overcome these issues [26; 27], typically, these approaches need more data sources than the time between failures, which makes them more challenging to implement in practical scenarios. Adopting overly conservative maintenance schedules to avoid all failures, known as working in the safety zone, leads to the under-utilization of the asset's useful life and, typically, is not cost-effective. Some research has focused on optimizing PM actions, especially in scheduling interventions to avoid impacts on production [28; 29; 30; 31; 32] or in grouping maintenance tasks [33]. The uncertainty of the distribution of the time between failures (TBF) [34] is addressed by [35], who uses a Bayesian approach to estimate the strength of the population of replacement parts, and by [36], who considers the asset's age to update the failure rate of parts. Some PM approaches also consider the health state of components by performing periodic inspections [37] or by using prediction models, such as the Wiener process model [38]. Other studies, such as [39; 40; 41; 42], focused on optimizing PM actions of repairable systemsby considering imperfect maintenance actions. Maintenance costs may be mitigated by considering opportunistic maintenance intervals with imperfect PM actions in systems whose unavailability caused by preparation time is considerable [43]. Despite recent efforts to optimize the scheduling of maintenance actions in the absence of a prognostic model, a persistent issue remains: the intervals between maintenance actions are maintained static.