## 2 Proposed Approach to Modeling POS Combinations in MUPSA
### Step 2: Development and Quantification of an Integrated Model for Each Unit  
In the second step, an integrated model for each unit is developed by combining its FP and LPSD PSA models into a single-top fault tree. The top event, in this case, is defined by a given risk metric and the IE to be analyzed. Figure 3 shows an example of an integrated single-unit model where the top event corresponds to core damage in Unit 1 due to a LOOP IE. Here, the following tasks should be performed to combine the FP and LPSD models into one and quantify it effectively.  
* Depending on the POS, gates with the same name may have different logic, and basic events with the same name may have different probabilities. Therefore, in order to distinguish such gates and basic events between POSs, \"POS identifiers\" are added to the names of all gates and basic events (e.g., \"XXX-P2\").
* \"POS basic events\" that represent the fraction of time spent in each POS are added (e.g., U1-FRAC-PO, U1-FRAC-P2, and U1-FRAC-P3 colored in yellow in Figure 3) and combined with the logic for the corresponding POS under AND gates. The fraction of time for each event can usually be calculated from the FP and LPSD SUPSA results, and the sum of these fractions should be 1.
* Since each unit can only be in one POS at a time, the POS basic events are modeled as mutually exclusive events, as shown in Figure 4. This modeling may not be necessary depending on the logic of the MUPSA model.  
After the integrated single-unit model combining FP and LPSD models is developed, the accident sequence frequencies are quantified to confirm that quantification can be performed within an appropriate time. If the quantification succeeds, it is necessary to review whether the results are consistent with those of the original FP and LPSD SUPSA.  
If the integrated single-unit model is very large or has very complex logic, such as logical loops, the quantification may fail to produce results within a reasonable time (e.g., an hour). In such cases, the integrated model should be simplified by screening out non-risk-significant accident sequences. The screening step highlighted in orange in Figure 2 is performed. This step can be entered from Steps 2, 3, or 4 and takes a stepwise approach that applies three levels of screening criteria according to the quantification results as follows.  
1. Individual accident sequences with a contribution greater than 0.1% to the given risk metric are selected as long as the sum of the contributions from the selected sequences is greater than 95%. (If the quantification fails again after applying this criterion, the second-level criterion is applied.)
2. Individual accident sequences with a contribution greater than 0.5% to the given risk metric are selected as long as the sum of the contributions from the selected sequences is greater than 95%. (If the quantification fails again after applying this criterion, the third-level criterion is applied.)
3. Individual accident sequences with a contribution greater than 1% to the given risk metric are selected as long as the sum of the contributions from the selected sequences is greater than 95%.  
These criteria were classified by considering both the contribution of individual accident sequences to a given risk metric and the sum of the contributions of the selected accident sequences. In the third-level criterion, 1% for the contribution of individual accident sequences and 95% for the summed contribution are taken from the definition of \"significant accident sequence\" used in the ASME/ANS PRA standard [15].  
Screening out an accident sequence can be done by either (1) removing the corresponding gate logic from the integrated fault tree model or (2) setting the gate logic to FALSE. Both ways produce the same results, but the time taken for quantification may differ.  
Figure 4: Example of modeling basic events representing the fraction of time for each POS as mutually exclusive events.  
Figure 3: Example integrated single-unit model combining FP and LPSD PSA models.