## 4 Analysis
### Sensitivity and Uncertainty Analyses of HOE Variables and ERL
#### 4.2.2 Uncertainty Analysis of HOE and ERL  
The purpose of the uncertainty analysis of the ERL is to determine the HOE-related influence on risk variations in the model. While the sensitivity analysis previously conducted assesses the ranking of the contributions of the HOE inputs to the total ERL outcomes, an uncertainty analysis assesses the uncertainty in the model risk outputs that arise from the variations in HOE inputs. One of the procedural requirements in a PRA is the quantification of the uncertainties associated with the model variables. In particular, the probability values of human and organizational failures are affected by high levels of errors in estimations. There is limited literature data supporting their inclusion in a PRA, both in terms of absolute value and in terms of distribution through the probabilistic model. It is therefore of the utmost importance to estimate the distribution and range of those errors and their impact on the global level of risk. The sensitivity results show that the most influencing HOE factors are 'not comply with instruction', 'deficient training' and 'inefficient emergency plan'. The three main variables determine important variations in the ERL of the system, up to 30% of the reference value. The minimum variations associated with the HOEs are in the order of 3-5%. The study indicates that HOEs have an important impact on the global risk level and cannot be neglected. Moreover, the more complex the system, the greater their influence. The complexity of the system is essentially due to the number of fire safety measures adopted, each of them subjected to varying maintenance regimes. The uncertainty analysis was performed based on the three most influencing HOEs identified in the sensitivity analysis in each case study. Using Case #4 as an example, when the most significant HOE factor of 'not comply with instruction' is simulated with 100 Monte Carlo simulations, the results are shown in Figure 10a where the y-axis represents probability values and x-axis represents the ERL values. It can be noted that the minimum probable ERL value with HOEs for Case #4 is 4.07 \(\times\) 10\({}^{-5}\) deaths/year while the maximum ERL value is 4.38 \(\times\) 10\({}^{-5}\) deaths/year. The mean value is 4.21 \(\times\) 10\({}^{-5}\) deaths/year and the standard deviation is 7.57 \(\times\) 10\({}^{-7}\). The 5% and 95% confidence interval range for uncertainty is between 4.09 \(\times\) 10\({}^{-5}\) and 4.34 \(\times\) 10\({}^{-5}\). When limited information is available on the likely distributions of the key variables, the triangular distribution can be used to reflect the most likely, lowest, and highest outcomes. When using a triangular distribution for the variable 'not comply with the instruction', the 5% and 95% uncertainty ranges between 4.06 \(\times\) 10\({}^{-5}\) and 4.32 \(\times\) 10\({}^{-5}\) as shown in Figure 10b. This indicates that a beta or triangular distribution does not alter the uncertainty range significantly while the beta distribution produces a smoother curve. When considering the three main HOE variables and assuming a beta probability distribution, the result is shown in Figure 11a. The y-axis represents the probability and x-axis represents the ERL values. It can be noted that the outcomes of the simulations are concentrated on the right side of the histogram. The standard deviation is small at \(5.40\times 10^{-7}\) with 5% and 95% uncertainty ranges from 4.15 \(\times\) 10\({}^{-5}\) to 4.30 \(\times\) 10\({}^{-5}\). The cumulative probability distribution of the single-run curve (S-curve) for Case #4 is presented in Figure 11b where the mean ERL is \(4.25\times 10^{-5}\). Figure 11c shows the probability density plot and Figure 11d shows the cumulative probability distribution of the three HOE input variables that have a major impact on the final ERL for Case #4.