## 3 Methodology
### Theory for Analyzing Incident Key Performance Indicators  
In the field of incident management, KPI is instrumental in assessing component performance. As detailed in [12], a large number of KPIs exist. For the scope of the presented analysis, the following indicators are of primary significance:  
* Mean Time To Failure (MTTF),
* Mean Time Between Failures (MTBF),
* Mean Time To Repair (MTTRep),
* Mean Time To Restore service (MTTRes). It is imperative to recognize that KPI terminologies and definitions can diverge notably among different suppliers and sectors. The association between these parameters, as detailed across multiple sources, is depicted in Figures 8 and 9. In the first figure is the connection between MTTRes, Mean Time To Identify (MTTI), Mean Time To Known issue (MTTK), MTTRep, and Mean Time To Validate (MTTV), while the subsequent figure emphasizes the relationship between MTBF, MTTRes, and MTTF. In the domain of incident management, MTBF and MTTF stand as paramount reliability metrics. These metrics offer insights into two distinct aspects: the expected time interval between two successive failures (MTBF) and the anticipated duration until a component's initial failure (MTTF). A salient distinction exists between them. Figure 8: Graphic display of the relationship between parameters MTBF, MTTRes, and MTTF. Figure 7: AG of the simplified interconnected test network. MTTF is predominantly applied to components that necessitate immediate replacement subsequent to a failure, and it is mathematically represented as  
\[\text{MTTF}=\frac{\Sigma T}{\Sigma n_{f}}, \tag{1}\]  
where \(\Sigma T\) signifies the total operating time and \(\Sigma n_{f}\) signifies the number of failures. Shifting the focus to the assessment of system availability, incident management teams generally concentrate on two primary KPIs: MTTRep and MTTRes. The former, MTTRep, elucidates the mean duration required to mend a system following the detection of a failure. It is defined as  
\[\text{MTTRep}=\frac{T_{rep}}{\Sigma n_{r}}, \tag{2}\]  
where \(T_{rep}\) signifies the cumulative time allocated for repairs and \(\Sigma n_{r}\) signifies the number of repairs. Contrastingly, MTTRes is indicative of the average time consumed to restore a system to its full operational capacity post incident. It is articulated as  
\[\text{MTTRes}=\frac{\Sigma T_{res}}{\Sigma n_{r}}, \tag{3}\]  
where \(T_{res}\) signifies the cumulative time allocated for restoring system operation. Lastly, MTBF finds its application with components that can be refurbished following a failure. Its definition is  
\[\text{MTBF}=\text{MTTF}+\text{MTTRes}. \tag{4}\]  
To accurately evaluate the availability and reliability of interconnected infrastructure, it is essential to concentrate on the most relevant parameters. In this regard, three pivotal parameters are identified for the analysis: MTTF, MTBF, and MTTRes. These metrics offer invaluable insights and present the most lucid information. Employing this consolidated methodology facilitates a better usage of KPI parameters. These parameters are related to events that impact the interrelated components of the infrastructure, encompassing power, communication, and control systems. This strategy not only deepens the comprehension of the foundational issues and their mutual interplay, but also amplifies the efficacy in troubleshooting and resolving events. The examined representative interconnected infrastructure is divided into three primary sections: (i) the power grid, (ii) the communication segment, and (iii) the control segment. For the context of this paper, Segments (ii) and (iii) are assessed collectively. The elements of Segment (i) are specified as follows:  
* HV/MV transformer (110/22 kV) labeled T1 is determined according to [26] as MTBF 26,310.709 h and MTTRes 4.403 h. The numbers are derived from study [17]. In the paper, \"MTBF\" corresponds to MTTF, and \"MTTR\" corresponds to MTTRes.