# Risk Index Method--A Tool for Building Fire Safety Assessments
## 2 Materials and Methods
### Fire Risk Index Calculation  
The last step of fire strategy evaluation is a calculation of a fire risk index (FRI). In the original Gretener method, fire risk was assumed as a product of hazard severity (fire hazard) and loss expectation represented by the fire frequency of ignition. In the presented method, the fire risk and fire hazard terms are replaced respectively by fire (strategy) risk index (FRI) and fire hazard index (FHI), but the general assumptions stay the same Equation (1) [40,41]. \[\text{Fire risk index (FRI) = Fire hazard index (FHI) \cdot Frequency of ignition (Fi)} \tag{1}\]  
The hazard severity referred to as the fire hazard index in Equation (1) is proportional to the potential hazard, reduced by protective measures Equation (2). \[\text{Fire Hazard Index (FHI) = (Potential Hazard (PH))/(Protective Measures (PM)} \tag{2}\]  
The original Gretener formula expressed empirically derived numerical factors for fire initiation and spread, with factors for fire protection. The idea used in the method presented here is based upon the values achieved from the scoring of each fire safety factor in accordance with Tables 3 and 4 for the baseline and actual strategies, respectively. Additionally, appropriate weighting factors for FRI and FHI calculations are applied (Table 5). The weighting factors are proportional to the baseline fire strategies values from Table 3 and their role is to keep the same hierarchies between several safety factors in the actual fire strategy as in baseline one. Figure 3: Fire strategy value grid for a shopping mall-example. Total scoring for protective measures (PM) is obtained from the formula Equation (3) by aggregating the points obtained from the assessment of each fire safety factor adjusted by the appropriate weighting factor from Table 5.  
\[\text{PM}=\Sigma\text{W}_{\text{i}}\text{E}_{\text{i}} \tag{3}\]  
where  
\(\text{E}_{\text{i}}\): \(\text{E}_{\text{ORG}}\), \(\text{E}_{\text{LIM}}\), \(\text{E}_{\text{PAS}}\), \(\text{E}_{\text{DET}}\), \(\text{E}_{\text{SUP}}\), \(\text{E}_{\text{SC}}\), \(\text{E}_{\text{MAL}}\), \(\text{E}_{\text{FB}}\)-score of each fire safety factor,  
\(\text{W}_{\text{i}}\): \(\text{W}_{\text{ORG}}\), \(\text{W}_{\text{LIM}}\), \(\text{W}_{\text{PAS}}\), \(\text{W}_{\text{DET}}\), \(\text{W}_{\text{SUP}}\), \(\text{W}_{\text{SC}}\), \(\text{W}_{\text{MAL}}\), \(\text{W}_{\text{FB}}\)-weighting factors from Table 5.  
By determining the result of the assessment of protective measures (PM), the value of the fire hazard index FHI, for both baseline and actual fire strategies can be calculated from the formula Equation (4). \[\text{FHI}=\text{PH}/\text{PM}\text{-}100 \tag{4}\]  
where  
\(\text{FHI}\)--fire hazard index,  
\(\text{PH}\)--potential hazard,  
\(\text{PM}\)--protective measures. The potential hazard is applied, respectively, to the building risk profile, in accordance with Table 6[40]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Objective** & **Risk Profile** & **Potential Hazard Factor (PH) 1 ** \\ \hline Life & A1 & 1.04 \\  & A2 & 1.08 \\  & A3 & 2.78 \\  & A4 & 6.13 \\  & B1 & 1.13 \\  & B2 & 1.51 \\  & B3 & 3.45 \\  & B4 & 6.70 \\  & C1 & 1.62 \\  & C2 & 1.83 \\  & C3 & 3.97 \\  & C4 & 6.83 \\ \hline Property & A/B/C1 & 0.58 \\  & A/B/C2 & 1.43 \\  & A/B/C3 & 3.82 \\  & A/B/C4 & 6.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Potential hazard factors appropriate for building risk profiles. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline
**Objective** & & & & & & & & & & & & & & & & & & \\ \hline
**Risk Profile/** & & & & & & & & & & & & & & & & \\
**Weighting Factor** & & & & & & & & & & & & & & & & \\ \hline W\({}_{\text{ORG}}\) & 0.6 & 0.6 & 2.0 & 4.0 & 1.2 & 1.6 & 2.4 & 3.4 & 0.8 & 0.6 & 1.8 & 3.2 & 0.8 & 0.8 & 2.8 & 3.6 \\ W\({}_{\text{LIM}}\) & 4.2 & 3.8 & 2.6 & 1.8 & 4.2  
The final step of the fire strategy assessment is the determination of the fire risk index from the formula Equation (5) [40; 41; 42; 43; 44; 45].