# Towards Optimizing Multi-Level Selective Maintenance via Machine Learning Predictive Models
## 2 Literature Review  
The main bodies of literature related to our study are selective maintenance (SM) and predictive maintenance (PdM). In the literature, the SM problem for multi-component systems was introduced by [PERSON] et al. [10]. The authors studied a serial-parallel system with identical components, the only maintenance strategy available is a replacement and the age of each piece of equipment is exponentially distributed. In addition, to solve the SM problem, the system degradation process is modeled stochastically following an exponential or Weibull distribution which is nearer to reality. [PERSON] et al. [11] supposed that system component life follows probability Weibull distributions and the decision making is given three maintenance types on failed components: minimal repair, replacement of failed components, and preventive maintenance. Otherwise, in many practical industrial conditions, the system health status and the lifetime distribution parameters of the components after the execution of such missions are uncertain [12; 13] and the resources (such as the time allotted to the break and budget) required to achieve maintenance actions are limited. So, the selective maintenance models have been used to increase the system performance and reduce life-cycle cost. Since most of the above works focused on binary systems, [PERSON] et al. [14; 15] proposed a new optimization approach to solve the SM problem for a multi-state serial-parallel system. The components as well as the system are considered multi-state, which is more realistic by considering the assumption of binary components. The objective is to minimize the total cost of maintenance by transiting from one state to another for each component and the system. Other SM studies proposed several maintenance options that can be performed to restore the component between AGAN and ABAO is known as imperfect maintenance. These approaches are essentially based on age-reduction models that combine an age-reduction approach with hazard adjustment [16; 17]. In this work, the authors developed an age reduction model with an imperfect maintenance action for selective maintenance. They proposed that the age reduction factor depends on the maintenance cost to reflect whether a component is comparatively young or old. So, the component effective age depends on this characteristic constant which helps to establish a relationship between the age reduction factor and component effective age and maintenance cost. We can notice that all the above-mentioned works propose a model-based approach, with the maintenance model based on theoretical parameters. More recently, with the emergence of new tools such as computer science and the Things Industrial Internet, the maintenance strategies adopted in industrial fields are evolving towards a new PdM policy and condition-based maintenance [7; 18; 19]. The concept of PdM is to predict the system's future state early enough based on its actual conditions. Several PdM approaches have been developed in the different production sectors in recent years. [PERSON] et al. [20] proposed a new approach for predictive health management of manufacturing systems based on the component's function. The concept of the predictive strategy involves, as a first step, determining the degradation instrument, functional dependence and remaining useful life (RUL) for the machine system. Then, an operation reliability-focused RUL prediction technique for production systems is established based on the functional dependency of the components. The selected maintenance strategy is based on dynamic RUL prediction, and the functional importance is performed to order the predictive maintenance of component sets. The proposed approach can guarantee the manufacturing system's ability to complete production operations with high-quality products as well as minimize the maintenance cost in the manufacturing cycle.