# A Robust Conformal Framework for IoT-Based Predictive Maintenance
## 1 Introduction  
In today's Industry 4.0 landscape, equipment, processes, and decision support systems (DSS) are seamlessly interconnected, with a vast amount of sensor data continuously collected in real time. This interconnectivity facilitates various applications (e.g., predictive maintenance), ultimately transforming traditional manufacturing into agile, data-driven systems. The IoT plays a pivotal role in this technological shift, utilizing sensor displacements and platforms to connect devices and gather data seamlessly, enabling intelligent analytics through AI. According to [PERSON] et al. [1], IoT facilitates the structuring of complex ecosystems, enabling data processing through five distinct layers (sensing, network, storage, learning, and application). The comprehensive review by [PERSON] and [PERSON] [2] also supports the structured logic mentioned by [PERSON], highlighting the crucial functions of the layers in the IoT pipeline, from the data source to the extraction of information. In most IoT architectures, the sensing layer gathers data through sensors and actuators, representing the physical part of the system, and disseminates data through the network layer, which extends the computation to other apparatuses such as cloud or fog systems. Then, the storage layer is responsible for caching and preserving data, whilethe learning layer employs information retrieval through advanced algorithms or data analysis. The DSS is supported by the application layer. It utilizes the valuable insight presented in a human-interpretable way to enhance practical applications or to be integrated into larger systems (e.g., networking, security, intelligent IoT). Although the layered IoT architecture mentioned above is relevant in many domains (from medical to agriculture), it is particularly beneficial when adopted in critical domains where timing responsiveness is pivotal (e.g., industrial maintenance). PdM, clearly born from the combination of AI and IoT, represents the paradigm shift from traditional maintenance strategies. The adoption of data-driven methodologies permits the forecasting of a system's future state, ergo estimating the machine degradation pattern (prognosis) [3; 4]. Conversely, this intelligent approach allows more complex anomaly detection methodologies (diagnosis) while seeking to optimize maintenance schedules, reduce unplanned downtime, and minimize production costs. Historically, this transformation originated from the past industrial revolutions. It commenced with simple strategies, such as reactive maintenance based on visual inspections by trained craftsmen and preventive maintenance based on planned routine operations, scheduled inspections, and performance monitoring [5]. In the last century, condition-based monitoring (CbM) appeared as a pioneering data-driven approach to more effectively monitoring the health and performance of machinery through sensors. It emerged as a branch of mechanical engineering, as highlighted in the seminal work by [PERSON] [6], and then was embraced as a branch of statistics, emphasizing the importance of data analysis in maintenance decision-making processes [7]. The operational deployment of this approach involves several critical steps, with parameter selection representing a pivotal stage to identify the most relevant variables indicating the condition of the machinery [8]. By processing the set of selected parameters, it is possible to generate potential condition indicators that represent the statistical properties of the process by providing quantifiable measures of equipment health [9]. Subsequently, quality control charts, baselines, and thresholds are set for monitoring deviations from normal operating conditions [10]. In practice, the later stage involves statistical techniques to determine these control limits, identifying regions of in-control conditions, thereby highlighting abnormal behavior in the alternative machinery's performance.