###### Abstract  
Maintenance has always been a key activity in the manufacturing industry because of its economic consequences. Nowadays, its importance is increasing thanks to the \"Industry 4.0\" or \"fourth industrial revolution\". There are more and more complex systems to maintain, and maintenance management must gain efficiency and effectiveness in order to keep all these devices in proper conditions. Within maintenance, Condition-Based Maintenance (CBM) programs can provide significant advantages, even though often these programs are complex to manage and understand. For this reason, several research papers propose approaches that are as simple as possible and can be understood by users and modified by experts. In this context, this paper focuses on CBM optimization in an industrial environment, with the objective of determining the optimal values of preventive intervention limits for equipment under corrective and preventive maintenance cost criteria. In this work, a cost-benefit mathematical model is developed. It considers the evolution in quality and production speed, along with condition based, corrective and preventive maintenance. The cost-benefit optimization is performed using a Multi-Objective Evolutionary Algorithm. Both the model and the optimization approach are applied to an industrial case. Keywords:condition-based maintenance; optimization; multi-objective evolutionary algorithms; production systems +
Footnote †: journal: Applied Soft  
In addition to what it is shown in Figure 1, in [5], an extensive review of condition-based maintenance research is performed using bibliometric indicators to show the increasing interest the topic is generating. A CBM strategy, where the optimal time to schedule a service visit is forecasted based on the condition of the equipment, is often proposed as an answer to the challenge of increasing the efficiency and reducing the cost of the equipment over their lifecycle. Therefore, CBM techniques are a key factor of maintenance. The recent literature concerning these terms is properly summarized in specific bibliographic reviews [6; 7; 8]. These studies promote implementation frameworks for CBM such as the one proposed in reference [4], which are appropriate for complex production systems based on data mining and machine learning. One of the conclusions extracted from the literature reviewed was that almost no emphasis has been given to the modeling of the relation between the production speed of equipment and its age or deterioration level. It is worth noting that, in the existing papers modelling the production speed loss (e.g., [9]), a linear relation between deterioration and speed is established. Nevertheless, in this research, and based on a different input justifying a nonlinear relationship between speed and aging [10], a new speed model is proposed. [PERSON] et al. [11] maintain that most existing literature either discusses CBM optimization of single component systems or focuses on technical issues about condition monitoring equipment and diagnosis. However, in this approach, a multi-component system will be approached. Therefore, overall, this paper focuses on the problem of the CBM optimization in a manufacturing environment, with the aim of determining the optimal deterioration levels beyond which PM activities should be applied under cost and profit criteria. The developed cost and profit model considers in a relatively simple way the interaction of production, quality and maintenance aspects of a multi-component single machine. The CBM model is applied to a plastic injection machine in a manufacturing plant using a Multiple-objective Optimization Problem (MOP) and optimized using a Multi-Objective Evolutionary Algorithm (MOEA). This paper is organized as follows: Section 2 introduces the proposed imperfect maintenance model, based on a Proportional Age Reduction (PAR) model, along with the calculation of the reliability parameters of a CBM maintenance strategy considering a PAR model.