## 5 Case Study
### Detailed Description of the SIRPM Model
The regressor employed in the decision tree model was a regression algorithm based on decision trees. The model's outputs, namely the failure predictions, directly influence the RPA processes of the machinery. When a failure is predicted, the RPA system triggers alerts to notify the maintenance team of potential intervention needs. The integration process between the machine learning model and the RPA system follows a continuous monitoring cycle, during which the performance of the model is periodically reviewed. With each adjustment or enhancement made to the ML model, the RPA system is updated to ensure the accuracy and efficiency of the integration. The MTBF (mean time between failures) is a metric that measures the average time between failures of a piece of equipment or system during its operation. The higher the MTBF, the better the system's reliability. The formula for calculating the MTBF is  
\[\text{MTBF}=\text{(Total Operating Time)}/\text{(Number of Failures)};\]  
where  
* Total Operating Time is the time during which the system or equipment is running without failures. * Number of Failures is the number of failures that occur during the considered time period. The MTTR (mean time to repair) is a metric that measures the average time required to repair a piece of equipment after a failure. The lower the MTTR, the faster the equipment is repaired and returned to operation. The formula for calculating the MTTR is  
MTTR = (Total Downtime)/(Number of Failures);  
where  
* Total Downtime is the total time during which the system or equipment was out of operation due to failures. * Number of Failures is the number of failures that occur during the considered time period. In the present study, calculations based on specific formulas were used to evaluate percentage reductions in different cost categories related to maintenance and operations. These calculations were performed based on the values provided by the company, with the following formulas applied:  
* The formula for calculating REDUCTION_Average Repair Costs is \(\text{REDUCTION\_Average Repair Costs \%= [1-[(\text{AFTER\_Average Repair Costs})]]}\times 100\);
* The formula for calculating REDUCTION_Total Maintenance Costs is \(\text{REDUCTION\_Total Maintenance Costs \%= [1-[(\text{AFTER\_Total Maintenance Costs})]]}\times 100\);
* The formula for calculating REDUCTION_Unplanned Downtime Costs is \(\text{REDUCTION\_Unplanned Downtime Costs \%= [1-[(\text{AFTER\_Unplanned Downtime Costs})]]}\times 100\); Downtime Costs)/(BEFORE\_Unplanned Downtime Costs)]]\(\times 100\);
* The formula for calculating REDUCTION_Total Operational Costs is \(\text{REDUCTION\_Total Operational Costs \%= [1-[(\text{AFTER\_Total Operational Costs})/(\text{BEFORE\_Total Operational Costs})]]}\times 100\);  
The first formula measures the percentage reduction in total operational costs over the analyzed period, reflecting the overall impact of the implemented strategies. The second formula calculates the reduction in costs associated with unplanned downtime, highlighting improvements in operational efficiency. The third formula evaluates the percentage decrease in total maintenance costs, offering a clear view of the cost-saving measures implemented. Lastly, the formula for average repair costs measures the percentage reduction by comparing the values before and after the improvements, showcasing the effectiveness of the interventions. Regarding sustainability metrics, the company identified and monitored five main criteria, namely energy consumption, CO2 emissions, waste produced, use of materials, and recycling rate. For each of these criteria, historical values were provided before and after the model was implemented. The percentage reduction was calculated based on the difference between the values before and after implementation, where the value obtained after implementation was divided by the previous value, subtracted from one and multiplied by 100. These calculations allow us to accurately measure the improvement in terms of sustainability.