## 3 Materials and Methods
### Using the Extended RPI to Propose a Qualitative Mitigation Index (QMI)
For example, these performance variables may be negatively impacted by other factors, such as heavy reliance on a particular individual for reliability, or the allocation of human and technical resources to other projects or activities. Therefore, it is important to measure the volatility of the reliability, availability, and resilience scores. For this purpose, a fourth performance variable, robustness, is introduced to correct the performance level according to the expected volatility. To evaluate this variable, the following question must be answered:  
* _Am I able to maintain the values for reliability, availability, and resilience with the available resources?_  
Table 1 summarizes the four questions defined for each of the four performance variables. The answers to these questions help to evaluate the performance variables, which can be done using the rating scales shown in Table 1.  
These four variables have an orthogonal relationship, i.e., their scope does not overlap, so their classification is mutually exclusive. Table 2 shows a 10-point rating scale for evaluating the performance variables described above on the basis of expert judgments (qualitative evaluation). In this way, the mitigation performance variables for a given failure mode of a given risk scenario are evaluated according to the experts' judgments using Table 2.  
Then, the qualitative mitigation index (_QMI_) for a given failure mode is calculated using Equation (13) (extended RPI) by replacing the risk variables with mitigation variables \begin{table}
\begin{tabular}{c c c} \hline \hline
**Mitigation Variables** & **Questions that Support the Ratings Given to** \\  & **Mitigation Variables** \\ \hline \multirow{4}{*}{Reliability} & Do I have the required knowledge, information, and \\  & & experience to perform consistently well and maintain \\  & & the required level of quality to avoid/mitigate the \\  & & analyzed failure mode? \\ \hline \multirow{4}{*}{Availability} & Given the available resources, do I have the necessary \\  & & human and technical resources to avoid the analyzed \\  & & failure mode? \\ \hline \multirow{4}{*}{Resilience} & Am I able to recover the level of reliability and available \\  & & performance when adverse events occur and make the \\  & & necessary changes within an acceptable period of time? \\ \hline \multirow{2}{*}{Robustness} & Am I able to maintain the values for reliability, \\  & & availability, and resilience with the available resources? \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Questions to rate mitigation variables. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Reliability** & **Availability** & **Resilience** & **Robustness** & **Ranking** \\ \hline Absolute Uncertainty & Absolute Uncertainty & Absolute Uncertainty & Absolute Uncertainty & 1 \\ Very Remote & Very Remote & Very Remote & Very Remote & 2 \\ Remote & Remote & Remote & Remote & 3 \\ Very low & Very low & Very low & Very low & 4 \\ Low & Low & Low & Low & 5 \\ Moderate & Moderate & Moderate & Moderate & 6 \\ Moderately High & Moderately High & Moderately High & Moderately High & 7 \\ High & High & High & High & 8 \\ Very high & Very high & Very high & Very high & 9 \\ Almost certain & Almost certain & Almost certain & Almost certain & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mitigation performance ratings, 10-point rating scale. and keeping the calculation process presented in Section 3.2. Equation (13) shows the expression for the _QMI_. \[QMI_{i}=\sum_{j=1}^{n-1}\left(\frac{w_{j}^{M}\cdot\epsilon^{n-j+1}+1}{\epsilon^{ n-j+1}}\cdot\delta_{ij}^{M}\right)+w_{n}^{M}\cdot\delta_{in}^{M} \tag{13}\]  
Here, the index \(M\) represents the mitigation variables and their respective weights. Using Equation (13) and considering the four mitigation variables--Reliability, Availability, Resilience, and Robustness, in that order--yields Equation (14), which estimates the degree of mitigation for each failure mode \(i\).