## 3 Case Study
### Example MUPSA Cases with Different Numbers of Units
#### 3.2.2 Results  
Table 4 summarizes the quantification results for five cases not applying the screening step, including the single-unit case. Here, the two risk metrics, site CDF and multi-unit CDF were calculated by the following equations, which are consistent with the definitions described in the IAEA safety report on MUPSA [3]:  
\[\text{(Site CDF)}=\sum\text{(1-unit CDF+2-unit CDF+\ldots+n-unit CDF)}, \tag{3}\]  
\[\text{(Multi-unit CDF)}=\sum\text{(2-unit CDF+\ldots+n-unit CDF)}, \tag{4}\]  
where \(n\) is the number of units included in MUPSA. The points of interest from Table 4 are as follows. * As the number of units involved increased, the model size, site CDF, and multi-unit CDF increased almost linearly while the run time and the number of MCSs increased exponentially. * The quantification for the SU-LOOP model with about 58,000 events succeeded to produce results in less than a minute, eliminating the need to screen out non-risk-significant accident sequences in Step 2. * For each number of units, the development of the MUPSA model in the form of a single-top fault tree was successful, so there was no need to go to the screening step in Step 3 either. * In the 2-unit, 4-unit, and 6-unit cases, the quantification of the MUPSA model successfully yielded results within a reasonable time without performing the screening step. However, in the 10-unit case, the quantification failed without screening. In the 10-unit case, the quantification succeeded after applying the first-level criterion described in Section 2.2, i.e., by screening out the accident sequences with a contribution of 0.1% or less to the CDF in each integrated single-unit model. In this case, about 80% of the accident sequences in each single-unit model were removed; hence the total number of events, or in other words the model size, decreased by about 43% to 327,622. The run \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Model** & **SU-LOOP** & **2U-LOOP** & **4U-LOOP** & **6U-LOOP** & **10U-LOOP** \\ \hline Model size (sum) & 58,084 & 114,308 & 228,304 & 342,299 & 570,494 \\ Number of gates & 37,112 & 71,826 & 143,652 & 215,477 & 359,127 \\ Number of basic & 20,972 & 42,482 & 84,652 & 126,822 & 211,367 \\ events & - & - & - & - & - \\ \hline Run time (sec.) & 56 & 155 & 639 & 2,001 & N/A \\ \hline Number of MCS & 221,374 & 771,915 & 2,902,484 & 6,618,173 & N/A \\ \hline Site CDF & 1.36 \(\times\) 10\({}^{-6}\) & 2.24 \(\times\) 10\({}^{-6}\) & 4.21 \(\times\) 10\({}^{-6}\) & 6.35 \(\times\) 10\({}^{-6}\) & N/A \\ \hline Multi-unit CDF & N/A & 9.68 \(\times\) 10\({}^{-8}\) & 1.72 \(\times\) 10\({}^{-7}\) & 2.70 \(\times\) 10\({}^{-7}\) & N/A \\ \hline \hline \end{tabular} Note: (1) The model size for each case is the sum of the number of gates and the number of basic events. (2) CPU used in quantification: AMD Ryzen 9, 3950X 16-core processor, 3.49 GHz.  
\end{table} 
Table 4: Comparison of quantification results by the number of units (without screening). time was 2345 s, and the total number of MCSs was about 25,000,000. The site CDF and multi-unit CDF were 1.01E-05/yr and 4.34E-07/yr, respectively. Although the 6U-LOOP model was successfully quantified without screening, the run time was over 2000 s. If the model size increases or the logic becomes more complex, the computation time could become an issue. Therefore, in order to examine how the quantification results including the run time change when the three screening criteria are applied, the 6U-LOOP model was modified by applying each criterion in turn and re-quantified. Table 5 compares the results according to the screening criteria. As the criterion level increased, by removing more and more non-risk-significant accident sequences, the model size and computation time decreased significantly, while the number of MCSs and the CDF values decreased relatively slightly. In particular, the multi-unit CDF was almost the same, with a difference of less than 1% between the four cases.