## 3 Case Studies
### Event and Fault Tree  
The ETA uses a logical technique to examine the failure and success of technical risks emanating from an event. The initial and subsequent events are assigned probabilities and possible outcomes contributing to computations of expected number of consequences. Typical fire safety sub-systems used in high rise buildings are fire detection systems, emergency notification systems, fire suppression systems, interior fire barriers, floor experimentation (vertical barriers) and building egress systems. The ET incorporates all fire safety sub-systems expected to be present within the high-rise residential buildings as they relate to occupant evacuation as well as the relevant FSVM design scenarios that are applicable to the case studies as follows: (i) CS--Concealed Space (ii) CF--Challenging Fire (iii) BE--Blocked Exit and (iv) Robustness Checks where RC1 is failure of detection, RC2 is failure of sprinklers and RC3 is failure of building alarm. Events are assumed to be independent of each other. The fire safety sub-systems in high-rise buildings are often provided with redundancies to avoid a single point failure. An efficient fire safety system will increase ASET and reduce RSET. The ET helps in identifying the critical sub-system path of fire safety that leads to better mitigation measures. A typical ET is shown in Figure 6. After the fire is initiated, the first branch is whether fire is in a concealed space or SOU/corridor with a probability of 0.2 and 0.8, respectively. In the next event, this fire can develop into a challenging fire (>5 MW) or a smouldering fire with a probability of 0.45 and 0.55, respectively. Further in the next event, failure of fire detection occurs with a probability of 0.1. Next in the chain comes the sprinkler system with a failure probability of 0.10. A building alarm failure occurs with a probability of 0.1. The probability of the next event, which is blocking of an exit, has a failure probability of 0.2. The failure probabilities assumed are slightly conservative compared to the literature (Appendix B, Table A4) and so will likely result in slightly higher, yet acceptable ERL values. In the worst credible case, the fire ignition occurs in a concealed space, developed into a full CF, the sprinkler system fails (robustness check) and the emergency exit is blocked (BE). In the best case scenario, the fire does not occur in a concealed space, but in the living room of the SOU, does not develop into a full CF, there is no failure in sprinkler or alarm or detection and the emergency exit is not blocked. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Building** & **Case \#2** & **Case \#3** & & **Case \#4** \\ \hline
**Characteristics** & **Performance** & **DTS** & **Performance** & **DTS** & **Performance** & **DTS** \\ \hline Occupants per floor & 24 & 24 & 54 & 54 & 58 & 58 \\ Number of floors & 24 & 24 & 23 & 23 & 21 & 21 \\ Floorplate area (m\({}^{2}\)) & 484 & 484 & 1099 & 1099 & 1343 & 1343 \\ Number of units/floor & 6 & 6 & 15 & 15 & 20 & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Characteristics of the building case studies. The frequency and number of fatalities are also shown in Figure 6. The two most critical events resulting into maximum number of deaths are CF and sprinkler failure. That is, if fire develops into a CF and sprinkler fails, it leads to maximum fatalities. A fire will not be controlled if the fire sprinkler system is not functioning properly. When the sprinkler system is activated, fire growth is controlled or extinguished. If the sprinkler system fails, the fire continues to grow until untenable conditions occur. The negative effects of a fire spreading throughout the building are directly related to the failure of each sub-system. Systems performing as intended will elongate the ASET giving occupants more time to reach safety. The number of consequences is dependent on the reliability of the detection, suppression, notification, containment, robustness and egress sub-system systems.