## 5 Case Study and Results
### Validation Strategy--Design of Experiments  
In the following paragraphs, the steps followed for the validation of the proposed framework in the real-life industrial scenario will be presented. Since maintenance is a very important aspect regarding the flawless and continuous operation of manufacturing systems, the validation strategy should be carefully designed and also should provide a quantified result of the impact. Therefore, for each of the machine-tools examined in this process, two basic metrics will be used. According to the guidelines given by [PERSON] in Reference [21] regarding the mathematical programming of manufacturing systems, the operating and maintenance costs for a machine can be calculated by the equation below. \[\textit{Operating and Maintenance Costs}=\ \sum_{t=1}^{T}(P/F,I,t)\sum_{i=1}^{N}m_{it}x_{it} \tag{3}\]  
where \((P/F,I,t)\equiv\) Present a worthy interest factor for discrete compounding when the discount rate is 1% per period and the discount interval is \(t\) periods. \(m_{it}\equiv\) The cost of operating and maintaining a machine of type \(i\) during period \(t\). Is the number of machines, on one hand, in the work center \(i\) for period \(t\). In order to quantify the outcome of the validation process for the proposed framework, each of the above-mentioned values will be calculated in order to conclude on the efficiency of the real-time remote maintenance. Therefore, the cost for operation and maintenance for a CNC milling machine has been calculated, based on data derived from a real-life machine-shop. The cost of operation and maintenance has been calculated on an annual basis for time horizon of five years, and the results are depicted in Figure 8. Additionally, in Figure 8, a prediction of the cost is made for the oncoming five years based on statistical regression, presented by the red dot trendline. It is stressed out that, due to the non-linear relation between the individual costs of operation and maintenance of machine tools during their lifecycle [37], a 2 nd degree polynomial has been calculated. The same calculations were made for the cost estimation based on the proposed methodology and, similarly, a prediction is made for future maintenance costs. As a result, with the proposed methodology, a reduction of approximately 100 k euros is feasible in a time span of 10 years, which indicates that the framework could eventually be implemented in manufacturing systems and improve their operation. Figure 8: Cost of operation and maintenance analysis. Besides the cost for operating and maintenance, another metric has been calculated and compared regarding the downtime of the above-mentioned machine. In manufacturing systems, time resources are equally important for the financial resources. Therefore, a maintenance scenario has been investigated. For this repair scenario, the machine tool breaks down at an unpredicted time. At that time, the production process for this machine stops and the expert engineer is called to come on-site, inspect the machine, and repair it. The same scenario has also been investigated, but instead of requesting an expert engineer to visit the machine shop, a remote support session is established, and the repair is conducted by the technicians available in the machine shop. In Figure 8, the distribution of time per maintenance task is displayed for each of the scenarios examined. From Figure 6, it is undeniable that a significant amount of time can be saved with the adoption of the proposed framework, as the time for travelling and inspection are considerably longer, which affects the overall time the machine tool has been off the production schedule. Through the use of Figure 9, it is intended to reflect the difference of time distribution between the two scenarios examined during the validation process of the proposed framework.