## 4 Application Example  
Figure 2 presents such a hybrid method prepared for an event scenario according to the logic-gate symbols from Figure 1, leading to a change in water quality in a supply network due to its loss of chemical or biological stability [26,27]. The meanings of the symbols in Figure 2 are as follows:  
* I is a protection barrier related to the identification of contamination through the monitoring of water quality in the supply network,
* II is a protection barrier related to a warning system targeted at the recipients of water,
* III is a protection barrier related to the methods of prevention via a crisis water-supply system. A comprehensive analysis was performed where the event-tree and fault-tree methods were combined through the hybrid model. The hybrid model's specific designations, based on [16,28,29] and featured in Figure 2, are presented in Tables 1 and 2 below. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Designation** & **Description** \\ \hline
1. & a & Event related to the occurrence of secondary pollution of water in the supply network \\
2. & b & Event related to the occurrence of sediment (growth) or biofilm \\
3. & c & Event related to the occurrence of adverse hydraulic conditions \\
4. & d & Event related to an unexpected change in water quality parameters \\
5. & e & Event related to a lack of water chemical stability \\
6. & f & Event related to a lack of water biological stability \\
7. & g & Event related to a loss of physical stability of water resulting in the limit value for water turbidity being exceeded (\(\geq\)0.8 NTU) \\
8. & h & Event related to the emergence of a water-quality situation with a Langelier Saturation Index value from \(-\)4 to \(-\)5 and from 3 to 4 \\
9. & i & Event related to a lack of water chemical stability of water with a Ryznar Index value of \(>\)8.5 and \(<\)5.5 \\
10. & j & Event related to a loss of chemical stability of water with a Strohecker Index value of more than 0.5 \\
11. & k & Event related to a lack of water biological stability with a biodegradable dissolved organic carbon (BDOC) \\
12. & l & Event related to a lack of water biological stability with a \(\sum\)N\({}_{\text{innovorganic}}\) value of \(\geq\) 0.2 gN/m\({}^{3}\) \\
13. & m & Event related to a lack of water biological stability with a PO\({}_{4}\)\({}^{3-}\) value more than 0.03 g PO\({}_{4}\)\({}^{3-}\)/m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Specific designations of the fault tree. Figure 2: Hybrid Model of logical trees after a peak event related to the secondary water pollution in the water supply system. Probability values were adopted on the basis of the analysis, expert knowledge, and data presented by [PERSON] in a monograph [10] detailing the percentages of raw and treated water samples, in which limit values for the food substrates adopted for the stability assessment were exceeded. For BDOC, the probability of the limit value of 0.25 gC/m\({}^{3}\) being exceeded is 0.583; for \(\sum\)N\({}_{\text{inorganic}}\), the probability of the limit value of \(\leq\)0.2 gN/m\({}^{3}\) not being exceeded is 0.159; and for PO\({}_{4}\)\({}^{3-}\), (\(\leq\)0.03 gPO\({}_{4}\)\({}^{3-}\)/m\({}^{3}\)) the corresponding value is 0.01.