## 3 Problem Formulation and Proposed Model
### The Proposed Model: Failure Probability Normalisation as a Function of the Next Scheduled Job
These networks are structured with one input node and one output node, with a variable number of hidden neurons to be determined. The input node receives as input the value of prognostic failure probability under the medium or heavy workload values, while the output one provides the failure probability that a soft workload value would have produced under the same degradation conditions. The difficulty of this activity is the identification of valid failure probability values for training these auxiliary networks. In addition, it should be noted that the effect of the workload on machine degradation might differ in different degradation stages. Hence, it is advisable to conduct some pre-tests on the monitored machines/equipment at the various degradation stages. As an example, by running three exemplars of a specific monitored machine/equipment, each one with a different workload value, it is possible to collect failure probability values under different workload values and within the various degradation stages. Although this approach may appear burdensome and expensive, it is worth noting that this data collection may occur during the regular operation of machines/equipment, as well as in future periods, allowing, in this way, a future update of the model itself. Hence, during its operation, the model knows the current scheduled job for the monitored machine/equipment and, if this job has an expected soft workload, it directly uses the failure probabilities provided from logistic regression to forecast the future output value. Otherwise, if the current job has an expected medium or heavy workload, the output value is then normalised according to the reference value with the help of the two auxiliary neural networks introduced above. This value is then used in the time series feed-forward neural network for forecasting the future failure probability. The output value of the prognostic model thus obtained is referred to as the reference workload (i.e., soft load) and it is necessary, therefore, to adjust this value to the expected workload of the next job. To this extent, two other auxiliary neural networks, trained to find the relationship between the reference workload value and the expected workload of the next scheduled job, may perform this adjustment. The final output of the model represents the forecasted failure probability values of the monitored machine/equipment. It effectively reproduces the continuous degradation process of the machine/equipment with the knowledge of the future scheduled workload. With this enhanced accuracy, the proposed tool may be \begin{table}
\begin{tabular}{c c} \hline \hline
**JOB** & **Expected Mechanical Load** \\ \hline Job 1 & Soft Load \\ Job 2 & Heavy Load \\ Job 3 & Soft Load \\ Job 4 & Medium Load \\ Job 5 & Heavy Load \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Technician completed example of mechanical load of the monitored machine. integrated into the production schedule activity of Industry 4.0 manufacturing plants (or even into CPSs themselves in an M2M setting), leading to more balanced scheduling of production resources.