## 3 Problem Formulation and Proposed Model  
### Problem Definition, Hypothesis, and General Purpose of the Model  
The interconnection opportunities introduced by Industry 4.0 show all their potentiality when continuous information exchange between CPSs is in place. The literature review declares that the most important feature of the fourth revolution is represented by the possibility of autonomous scheduling and (potentially) rescheduling in CPSs within a short period, to avoid, for instance, an unscheduled stop or a safety accident. In order to make this prospect concrete, it is essential to have in-depth knowledge of the CPS itself, with a prognostic tool able to predict the likelihood that an industrial asset may complete a predefined job.  
Within the literature, the remaining useful life (RUL) is a well-established reference parameter in equipment prognostics. However, the Industry 4.0 capabilities agree to avoid the use of this parameter, uncertain of its nature, favouring the estimation of a failure probability value. This value, strictly related to the health state of the equipment, may allow a more efficient balancing between production and maintenance activities. Every component or equipment usually produces several kinds of signals when working conditions change over time (e.g., a higher temperature, different vibrations, or significant acoustic emissions). The problem is that there are many different equipment types, and, in a real vision, every equipment owns its history and its behaviour, due to previous unbalanced workload and uncertain material properties.  
Therefore, the design of a prognostic algorithm, able to consider a different kind of workload reassuming it in a single value, is desirable. This value should reflect the failure probability of the future workload to be scheduled on the machine, resulting in a sort of equipment degradation indicator. This physical feature and, most of all, methodology to be calculated must be universally applicable on each CPS and not dependent on its specific technological processing, both for general reasons of plant maintenance management and certain reasons of communication policy between CPSs. From a theoretical perspective, it would be possible to conceive a particularised prognostics algorithm for each set of machines. However, this paper aims to derive a data-driven model that could be easily adapted to whatever machine and operational scenario, only by changing the involved training dataset.  
The proposed self-detected condition-based maintenance (SdCBM) policy needs four main requirements to be developed [Figure 2]:  
* Cyber-physical system signal acquisition;
* Degradation modelling of the monitored machine/equipment;
* Prognostics generation model;
* Failure probabilities normalisation as a function of the next scheduled job.  
In agreement with the previously discussed requirements for a widely applicable model that can be concretely implementable in a production plant, the main and most significant effort of this paper consists of achieving a model both able to respect all the emerged hypotheses and constraints, to be composed of tools largely used and computationally consolidated, and to provide a feature strictly related to the RUL, but innovatively defined by an appropriate combination of the selected computational tools.