## 3 Problem Formulation and Proposed Model
### The Proposed Model: Failure Probability Normalisation as a Function of the Next Scheduled Job  
The introduced model can be successfully applied in industrial settings to forecast the future failure probabilities of monitored machines/equipment, considering their performance history and without any information about their future workloads. Thus, the approach presented at this point is capable of functionally extending the prognostic algorithms already available in the literature. Indeed, while the previous steps of the introduced approach are easily replaceable with alternative algorithms and methodologies, we would like to concentrate here on further improving the quality of the predictions by providing these prognostic algorithms with a new piece of information, i.e., the workload, both completed and to be completed. For instance, while forecasting the failure probabilities of a machine whose recent workload has been considerably slight, the prevision error produced by the model could be relevant, especially in the case of value underestimation (e.g., due to a sudden increase in the mechanical load of next scheduled jobs). For improved accuracy, it would be better to categorise machines into different categories according to the type of loads they are subject to. In the presence of stationary workloads, which may determine a slight or proportional change to a machine's working conditions, the model does not require any amendment (the workload influence turns out to be negligible in this scenario). Under variable workloads, however, the consideration of previous and future workload values for the monitored machine/equipment could be relevant for accuracy enhancement. Potential better performance of the proposed prognostic approach would benefit the algorithm for machine/equipment job scheduling as well. It may consider, as a further variable, the failure probabilities of workloads associated with the various jobs to be scheduled. This may lead to a more efficient utilisation of machines while reducing their RUL under a controlled risk of failure. Hence, we must tackle the new issue of finding the relationship between the failure probabilities, as derived from the logistic regression, and the workload values corresponding to the future scheduled jobs of the monitored machine/equipment. From an operational point of view, the scheduled job is only an indication of the operations the machine/equipment has to perform in the immediate future. Therefore, identifying and classifying all the possible jobs from a workload perspective turns out to be an important activity. An expert technician, with specialised knowledge of the considered machine/equipment, may complete this activity in the initial stage of project development. However, this same task could be carried out with the help of a pattern recognition neural network. As an example, in the case of three different workload values (soft, medium, and heavy load) for the monitored machine/equipment, it would be easy for the technician to find the relation between the various jobs and their expected workload (e.g., mechanical load) on the machine (Table 1). Although different classifications of machine workload values could be considered, once the relationship mentioned above is established, it will be necessary to introduce this information into the prognostic model. Among the several different technical opportunities, we chose neural networks as the tool to accomplish the task of identifying the link between the future expected workload values and one chosen as a reference. Taking the soft workload value as reference (Table 1), two feed-forward neural networks would be necessary: the first one to find the relationship between the medium workload and the reference workload and the second one to find the other relationship between the heavy workload and the reference workload. The number of hidden neurons and the combination of activation functions for these new neural networks can be found with a trial and error approach similar to that cited in the previous subsection.