## 1 Introduction
### Considerations in the Preparation of the Predictive Maintenance Plan
Deep belief networks (DBN), introduced by [38], is a type of neural network widely employed in predictive maintenance tasks due to their hierarchical learning capability, which enables capturing long-range dependencies--primarily in unsupervised learning. This architecture can be used in both supervised and unsupervised frameworks, being mainly applied for data dimensionality reduction and classification [39; 40]. However,DBNs are not suitable for time series prediction, as they have been outperformed by deeper architectures such as LSTMs and Transformers [41; 42]. Unlike traditional statistical forecasting methods such as autoregressive moving average (ARMA) [43], autoregressive integrated moving average (ARIMA) [44], autoregressive integrated moving average with exogenous variables (ARIMAX) [45], and exponential smoothing [46], which are typically limited as they rely on a sole time series, neural networks provide a promising solution for handling massive data [47], and they are characterized by multiple layers that enable complex feature abstraction from data points [48]. For the purpose of anticipating possible problems, [PERSON] and [PERSON] [49] indicates that smart maintenance within Industry 4.0 is oriented towards self-learning, failure prediction, diagnosis, and triggering maintenance programs. At the same time, [PERSON] et al. [50] identifies the suitability of its application since the utilization of supervised models for making forecasts will ensure that the process operates correctly and efficiently without incurring high maintenance costs and reducing product or assets degradation. Machine learning refers to the set of techniques and methods used by computers to autonomously extract complex patterns and relationships from large datasets and make decisions or predictions about real-world events [51]. The concepts used in machine learning are cross-disciplinary and come from computer science, statistics, mathematics, and engineering. The main types of machine learning were outlined by [52], and predictions are made based on new or unanticipated data [53] using labeled dataset. Deep learning is a branch of machine learning that focuses on the learning of data representations and of hierarchical features. With the objective of extracting features, deep learning algorithms employ a system comprising numerous layers of nonlinear processing identities (neurons) that aid in data abstraction [54]. Although recurrent neural networks in their various forms have traditionally been used, architectures equipped with attention mechanisms commonly used in natural language processing, which are more complex and have a higher number of trainable parameters, should provide better results [55]. The full discussion of Transformer-based neural networks for time series prediction can be found in [56]. For a comprehensive analysis of machine learning strategies and their application to predictive maintenance in sustainable manufacturing, readers may consult references [57; 58]. The optimization of neural network hyperparameters is conducted through Design of Experiments (DoE) methodology, with the dual objective of maximizing model performance, while ensuring operational simplicity to facilitate adoption by practitioners with limited technical expertise in machine learning. The implementation of this combination of solutions requires careful consideration and resolution of several difficulties, including the choice of technology to invest in, the management of current knowledge, its transfer, and the acquisition of new expertise [59; 60] describes the implementation of a roadmap that optimizes the likelihood that these tools will be applied successfully. These improvements are benchmarked against traditional forecasting methods like ARIMAX, a generalized ARIMA framework that integrates exogenous variables to improve predictive capability.