## 4 Analysis
### Sensitivity and Uncertainty Analyses of HOE Variables and ERL
#### 4.2.2 Uncertainty Analysis of HOE and ERL
The cumulative probability plot in Figure 11d indicates that the distribution of the probability for 'not comply with the instruction' is centred on higher values than the other two HOE variables; its mean is 0.46 compared to 0.25 for 'deficient training' and 0.11 for 'inefficient emergency plan'. Moreover, it is evident that the HOE variable 'not comply with the instruction' has larger variations than the other two because the difference between the 95% and the 5%-percentiles is 0.49 in absolute terms (and 1.07 relative to the mean). (Refer to Appendix C for detailed calculations). To evaluate the uncertainty of the model due to the three variables, these values can be compared with the output of the model from the Monte Carlo simulation. In Figure 11d, the graph indicates that the difference between the 95% and the 5% value is \(2.9\times 10^{-7}\). (Refer to Appendix C for detailed calculations). As expected, the HOE variable 'not comply with instructions' has the greatest influence on the outcome with a sensitivity of 5% followed by 'deficient training' at 4% and 'inefficient emergency plan' at 3%. Figure 10: Case #4: Uncertainty analysis for ’not complying with instructions’. (**a**) ERL uncertainty analysis for Case #4 with beta distribution. (**b**) ERL uncertainty analysis for Case #4 with triangular distribution. The Monte Carlo simulation runs for the ERL uncertainties for Case #1 to #4--DTS, performance and HOE solutions are plotted in the cumulative probability plots in Figure 12. It is observed that ERL for the performance solution with HOEs is higher as compared to the performance solution and DTS-based ERL values. Further, the performance solution (without HOEs) gives lower ERL as compared to the DTS solution. The results for different cases are summarized below:  
* For Case#1 ERL values for the performance solution with HOEs for 5% and 95% bounds are 4.21 \(\times\) 10\({}^{-5}\) and 4.58 \(\times\) 10\({}^{-5}\), respectively. ERL values for the DTS solution for 5% and 95% bounds are 3.10 \(\times\) 10\({}^{-5}\) and 3.37 \(\times\) 10\({}^{-5}\), respectively. Similarly, ERL values for the performance solution for 5% and 95% bounds are 2.94 \(\times\) 10\({}^{-5}\) and 3.18 \(\times\) 10\({}^{-5}\), respectively. From the average value, the ERL for the performance solution with HOEs is higher by 35% compared to the DTS solution and by about 44% as compared to performance solution. * For Case#2 ERL values for the performance solution with HOEs for 5% and 95% bounds are 4.40 \(\times\) 10\({}^{-5}\) and 4.63 \(\times\) 10\({}^{-5}\), respectively. ERL values for the DTS solution for 5% and 95% bounds are 3.91 \(\times\) 10\({}^{-5}\) and 4.10 \(\times\) 10\({}^{-5}\), respectively. Similarly, ERL values for the performance solution for 5% and 95% bounds are 3.78 \(\times\) 10\({}^{-5}\) and 3.97 \(\times\) 10\({}^{-5}\), respectively. From the average value, the ERL for the performance solution with HOEs is higher by 13% as compared to the DTS solution and by about 16% as compared to performance solution. Figure 11: (**a**) Uncertainty analysis of 3 main HOE variables -Case #4. (**b**) Single Cumulative probability plot of ERL Case #4 HOE. (**c**) Probability plots of significant HOEs for Case #4 (**d**) Cumulative distribution plots for significant HOEs –Case #4. * For Case#3 ERL values for the performance solution with HOEs for 5% and 95% bounds are 3.01 \(\times\) 10\({}^{-5}\) and 3.15 \(\times\) 10\({}^{-5}\), respectively. ERL values for the DTS solution for 5% and 95% bounds are 2.58 \(\times\) 10\({}^{-5}\) and 2.72 \(\times\) 10\({}^{-5}\), respectively. Similarly, ERL values for the performance solution for 5% and 95% bounds are 2.10 \(\times\) 10\({}^{-5}\) and 2.22 \(\times\) 10\({}^{-5}\), respectively. From the average value, the ERL for the performance solution with HOEs is higher by 16% as compared to the DTS solution and by about 41% as compared to performance solution.