Skip to content

03-example-1.mdx

Latest commit

 

History

History
961 lines (928 loc) · 44.7 KB

03-example-1.mdx

File metadata and controls

961 lines (928 loc) · 44.7 KB
title Example 1 - Single Failure Mode

import Link from "@docusaurus/Link"; import addBaseUrl from "@docusaurus/useBaseUrl"; import Citation from "@site/src/components/Citation"; import CitationFootnote from "@site/src/components/CitationFootnote"; import Figure from "@site/src/components/Figure"; import FigureInline from "@site/src/components/FigureInline"; import FigReference from "@site/src/components/FigureReference"; import NavContainer from "@site/src/components/NavContainer"; import ProcessList from "@site/src/components/ProcessList"; import TableReference from "@site/src/components/TableReference"; import TableVertical from "@site/src/components/TableVertical"; import VersionSelector from "@site/src/components/VersionSelector";

<NavContainer link="/desktop-applications/rmc-totalrisk" linkTitle="RMC-TotalRisk" document="desktop-applications/rmc-totalrisk/applications-guide"

Example 1 - Single Failure Mode

The first example illustrates the basic steps of setting up a risk analysis for a single hydrologically driven potential failure mode (PFM) of backward erosion piping (BEP) in RMC-TotalRisk. The spillway gates were assumed to operate as intended (100% reliability) for this risk analysis.

Hazards

The hydrologic hazard is represented by a stage frequency curve and provided in tabular format. Relationships for the 5th percentile, 50th percentile, and 95th percentile annual exceedance probabilities (AEP) were provided for each stage. To begin building the model, add a tabular hazard function as demonstrated in the following steps and in .

<ProcessList items={[ //Step 1 { title: ( <> Right-click on the Hazards folder in the Project Explorer window and select Add Tabular Hazard... Name the hazard function in the prompt (e.g., Stage Frequency) and press OK. </> ), }, //Step 2 { title: ( <> The hazard for the stage frequency curve is stage and is measured in feet. In the Tabular Hazard Properties section of the Properties window, (a), select Stage for Hazard Type and ft for Hazard Units. The stage frequency data contains fixed stages and uncertainty for the AEP values. Since uncertainty is defined for the probabilities in the stage frequency relationship and not the hazard, uncheck the Hazard is Uncertain check box. </> ) }, //Step 3 { title: ( <> The stage frequency curve is generally plotted on a normal probability-linear scale (i.e., AEP plotted on the x-axis on a normal probability scale and stage plotted on the y-axis on a linear scale). In the Interpolation Transforms section of the Properties window, the Hazard is set to  None (linear interpolation), and the Probability is set to Normal Z-variate, (b). </> ) }, //Step 4 { title: ( <> Select an appropriate input distribution that best defines the stage frequency dataset and enter the data into the hazard function. Uncertainty in the AEP is defined by 5th, 50th, and 95th percentile values. PERT-Percentile Z is selected from the Distribution drop-down menu as is typical for this type of analysis. Enter the hazard function from by copying and pating into the table as indicated in (c). </> ) } ]} />

{/Figure 1/}

{/Table 2/} <TableVertical tableKey="example-1-stage-frequency" caption="Stage frequency hazard function." alt="Stage frequency hazard function at the 5th, 50th, and 95th Percentile AEP." widthMode="intrinsic"

headers={[ [ { value: 'Stage (ft)' }, { value: '5th Percentile AEP' }, { value: '50th Percentile AEP' }, { value: '95th Percentile AEP' } ] ]} columns={[ [ 640.35, 640.89, 641.16, 641.28, 641.62, 641.86, 642.77, 642.93, 643.12, '643.30', 643.58, 643.72, 643.86, '644.00', 644.14, 644.16, 644.26, 644.51, 644.53, 644.56, 644.58, 644.71, 644.78, 644.87, 644.95, 645.04, 645.13, 645.29, 645.87, 646.64, 648.14, 650.65, 650.93, 652.01, 652.37, 652.77, 653.14, 653.78, 653.96, '654.10' ], [ "9.33E-01", "7.49E-01", "5.56E-01", "4.68E-01", "2.73E-01", "1.92E-01", "9.32E-02", "8.43E-02", "7.50E-02", "6.49E-02", "4.59E-02", "3.60E-02", "2.70E-02", "1.75E-02", "8.28E-03", "6.99E-03", "2.56E-03", "1.04E-03", "9.48E-04", "7.93E-04", "6.99E-04", "1.63E-04", "1.00E-04", "8.68E-05", "7.52E-05", "6.21E-05", "5.00E-05", "4.58E-05", "3.32E-05", "2.52E-05", "1.60E-05", "7.33E-06", "6.54E-06", "3.48E-06", "2.71E-06", "2.01E-06", "1.33E-06", "6.00E-07", "4.81E-07", "3.95E-07" ], [ "9.48E-01", "7.88E-01", "5.92E-01", "4.93E-01", "3.12E-01", "2.20E-01", "1.20E-01", "1.08E-01", "9.60E-02", "8.52E-02", "6.45E-02", "5.37E-02", "4.17E-02", "2.79E-02", "1.43E-02", "1.24E-02", "6.18E-03", "3.00E-03", "2.75E-03", "2.40E-03", "2.19E-03", "6.92E-04", "6.41E-04", "5.77E-04", "5.20E-04", "4.58E-04", "4.00E-04", "3.75E-04", "2.99E-04", "2.52E-04", "1.83E-04", "1.13E-04", "1.07E-04", "7.37E-05", "6.31E-05", "5.16E-05", "4.03E-05", "2.49E-05", "2.14E-05", "1.90E-05" ], [ "9.66E-01", "8.22E-01", "6.32E-01", "5.39E-01", "3.49E-01", "2.68E-01", "1.45E-01", "1.33E-01", "1.19E-01", "1.06E-01", "8.49E-02", "7.32E-02", "5.74E-02", "4.00E-02", "2.34E-02", "2.11E-02", "1.40E-02", "6.23E-03", "5.78E-03", "5.18E-03", "4.72E-03", "2.45E-03", "1.98E-03", "1.91E-03", "1.84E-03", "1.76E-03", "1.68E-03", "1.59E-03", "1.23E-03", "9.50E-04", "7.68E-04", "5.39E-04", "5.17E-04", "3.92E-04", "3.49E-04", "3.07E-04", "2.56E-04", "1.78E-04", "1.58E-04", "1.43E-04" ] ]} />

Transforms

The stage frequency, system response, and consequence data for this risk analysis are all a function of stage (ft). Therefore, a transform function is not required for this analysis.

System Responses

The system response probabilities for the backward erosion piping potential failure mode were obtained from team elicitation using the event tree method. The elicited system response probabilities are shown in , and the corresponding failure mode event tree is shown in .

{/Table 3/} <TableVertical tableKey="example-1-bep-srp" caption="Backward erosion piping system response probabilities organized by node and Stage in feet." alt="Backward erosion piping system response probabilities." headerAlign={["center", "center", "center", "center", "center", "center", "center", "center"]} headers={[ [ { value: "Stage (ft)", colSpan: 2, rowSpan: 1 }, { value: "641.00", colSpan: 1, rowSpan: 1 }, { value: "642.50", colSpan: 1, rowSpan: 1 }, { value: "644.00", colSpan: 1, rowSpan: 1 }, { value: "645.50", colSpan: 1, rowSpan: 1 }, { value: "647.50", colSpan: 1, rowSpan: 1 }, { value: "649.65", colSpan: 1, rowSpan: 1 }, ] ]} columns={[ //Stage (ft) [
{ value: ( <> Node 1
Continuous Pathway
Distribution: Triangular </> ), rowSpan: 4 }, null, null, null, { value: ( <> Node 2
Unfiltered Exit Downstream
Distribution: Deterministic </> ), rowSpan: 4 }, null, null, null, { value: ( <> Node 3
Initiation
Distribution: Triangular </> ), rowSpan: 4 }, null, null, null, { value: ( <> Node 4
Progression (Mechanical)
Distribution: Triangular </> ), rowSpan: 4 }, null, null, null, { value: ( <> Node 5
Progression (Hydraulic)
Distribution: Triangular </> ), rowSpan: 4 }, null, null, null, { value: ( <> Node 6
Unsuccessful Intervention
Distribution: Triangular </> ), rowSpan: 4 }, null, null, null, { value: ( <> Node 7
Breach
Distribution: Triangular </> ), rowSpan: 4 }, null, null, null, { value: ( <> Mean SRP w/ Intervention </> ), colSpan: 2 }, { value: ( <> Mean SRP w/o Intervention </> ), colSpan: 2 } ], //Stage (ft) [ "LRV", "MLV", "HRV", "EV", "LRV", "MLV", "HRV", "EV", "LRV", "MLV", "HRV", "EV", "LRV", "MLV", "HRV", "EV", "LRV", "MLV", "HRV", "EV", "LRV", "MLV", "HRV", "EV", "LRV", "MLV", "HRV", "EV", null, null ], //641.00 [ '0.030', 0.095, '0.450', 0.192, { value: "---", colSpan: 6 }, // Expanding across the remaining columns in a "merged" format 0.999, { value: "---", colSpan: 6 }, 0.999, '0.000', '0.000', '0.000', '0.000', '0.500', '0.750', 0.999, '0.750', '0.000', '0.000', '0.000', '0.000', 0.005, '0.050', '0.050', 0.035, '0.000', '0.000', '0.000', '0.000', "0.00E+00", "0.00E+00" ], //642.50 [ '0.030', 0.095, '0.450', 0.192, { value: "---", colSpan: 6 }, // Expanding across the remaining columns in a "merged" format 0.999, { value: "---", colSpan: 6 }, 0.999, '0.010', '0.050', '0.100', 0.053, '0.500', '0.750', 0.999, '0.750', 0.002, '0.010', '0.100', 0.037, '0.010', '0.070', '0.100', '0.060', 0.015, 0.075, '0.200', 0.097, "1.66E-06", "2.76E-05" ], //644.00 [ '0.030', 0.095, '0.450', 0.192, { value: "---", colSpan: 6 }, // Expanding across the remaining columns in a "merged" format 0.999, { value: "---", colSpan: 6 }, 0.999, '0.050', 0.075, '0.250', 0.125, '0.500', '0.750', 0.999, '0.750', 0.005, '0.040', '0.200', 0.082, '0.010', '0.070', '0.100', '0.060', '0.100', '0.200', '0.500', 0.267, "2.34E-05", "3.91E-04" ], //645.50 [ '0.030', 0.095, '0.450', 0.192, null, 0.999, null, 0.999, '0.090', '0.300', '0.500', 0.297, '0.500', '0.750', 0.999, '0.750', '0.010', 0.075, '0.300', 0.128, '0.050', '0.200', '0.600', 0.283, '0.200', '0.600', '0.900', 0.567, "8.77E-04", "3.10E-03" ], //647.50 [ '0.030', 0.095, '0.450', 0.192, null, 0.999, null, 0.999, '0.200', '0.600', '0.850', '0.550', '0.500', '0.750', 0.999, '0.750', 0.015, '0.090', '0.350', 0.152, '0.900', '0.990', 0.999, 0.963, '0.800', '0.950', 0.999, 0.916, "1.06E-02", "1.10E-02" ], //649.65 [ '0.030', 0.095, '0.450', 0.192, null, 0.999, null, 0.999, '0.500', '0.750', '0.900', 0.717, '0.500', '0.750', 0.999, '0.750', '0.020', 0.095, '0.400', 0.188, '0.900', '0.990', 0.999, 0.963, '0.900', '0.990', 0.999, 0.963, "1.64E-02", "1.70E-02" ] ]} />

{/Figure 2/}

To build the event tree system response function for the BEP PFM, use the following procedure:

<ProcessList items={[ { //Step 1 title: ( <> Right-click on the System Response folder in the Project Explorer window and select Add Event Tree Response... Name the system response function in the prompt (e.g., Backward Erosion Piping with Intervention). RMC-TotalRisk contains a database of event trees for common potential failure modes that can be used for system response functions. For BEP, select Flood from the Category drop-down menu and select Backward Erosion Piping from the Template drop-down menu and press OK. </> )
}, { //Step 2 title: ( <> The hazard for the system response function is stage and is measured in feet. In the Event Tree Properties section of the Properties window, (a), select Stage for Hazard Type and ft for Hazard Units. </> ) },
{ //Step 3 title: ( <> In the Interpolation Transforms section of the Properties window, select interpolation methods that are best suited for the hazard and system response probability. For this PFM, the Hazard is set to None (linear interpolation), and the Probability is set to Logarithmic, (b). </> ) }, { //Step 4 title: ( <> Assign the hazard levels that define the system response curve to the event tree by clicking on the Hazard node symbol, (c), and entering the hazard levels into the Hazard Levels section of the Properties window, (d). Alternatively, hazard levels can be assigned by hovering over the Initiating Hazard node name, clicking the Branch Properties symbol, and entering the hazard levels into the Hazard Levels section of the pop-up box that appears. The BEP PFM uses six hazard levels to define the system response curve as shown in . Click the add row symbol to add a new row to the bottom of the hazard level table. </> ), freeform: ( <> {/Figure 3/}

</> ), }, { //Step 5 title: ( <> Ensure the structure of the event tree, including the number, name, and description of each node, matches the potential failure mode being evaluated. To add a branch to the event tree or delete a branch from the event tree, click on the symbol and perform one of the following options: </> ), child: [ //Step 5a { title: ( <> Click the Add new branch button (to add a branch) or the Delete all branches from this node button (to delete branches) in the node toolbar, (a). </> ) }, //Step 5b { title: ( <> Click the Add Branch Node button (to add a branch) or the Delete Branch button (to delete branches) in the Sub-Branches section of the Properties window, (b). </> ) } ] }, { //Step 6 title: ( <> The Name and Description of the node can be changed in the Select Branch Properties section of the Properties window, (c), or by clicking the Branch Properties symbol. </> ),
freeform: ( <> {/Figure 4/} </> ), }, { //Step 7 title: ( <> Edit the nodal properties and enter system response probabilities for each node from into the event tree. Select an event tree node by clicking on the event tree node symbol or name, (a). Assign system response probabilities using the options located in the System Response section of the Properties window, (b). The Source and Distribution options for the system response probabilities should be assigned to fit the probabilities estimated by the risk assessment team. Node 1 in the BEP PFM is a stage-independent node, indicating that the probabilities do not change with stage, and was estimated with a minimum or lowest reasonable value (LRV), most likely value (MLV), and a maximum or highest reasonable value (HRV). The Source for Node 1 is set to Single Value  and the Distribution is set to Triangular. </> ), freeform: ( <> {/Figure 5/} </> ), },
{ //Step 8 title: ( <> The system response probabilities for Node 2 in the BEP PFM event tree are stage-independent but are only represented by a most likely value wthout a probability distribution. To assign system response probabilities for Node 2, the Source is set to Single Value and the Distribution is set to Deterministic, . The system response probabilities for Node 3 are stage-dependent (i.e., the probabilities change with stage) and are represented by a LRV, MLV, and HRV. For Node 3, the Source is set to Multi Value and the Distribution is set to Triangular, . Assign the system response probabilities for the remaining nodes of the event tree using the same procedure. </> ),

    freeform: ( <> 
    <Figure 
      docId="03-example-1-hazards.mdx"
      figKey="example-1-bep-node-inputs"
      src="figures/desktop-applications/rmc-totalrisk/applications-guide/v1.0/figures/figure6.png" 
      alt="Backward erosion piping event tree Node 2 (left) and Node 3 (right) inputs." 
      caption="Backward erosion piping event tree Node 2 (left) and Node 3 (right) inputs." />
    </> ), 
}, 
{ //Step 9
		title: (
    <> 
      Once the event tree has been completed, click on the <strong>Response</strong> tab within the event tree window to view a graph of the system response curve plotted against
      stage. The mean system response curve is plotted with a blue dashed line, <FigReference figKey="example-1-bep-srp-plot" />(a), and the
      90% confidence bounds are shaded in light blue, <FigReference figKey="example-1-bep-srp-plot" />(b). This curve can be compared against
      the system response probability input data to ensure accuracy. To change the graph axis extents, axis type, or axis properties, right click on the axis of
      interest and click <em>Format Axis: [Axis Name Here]</em>, <FigReference figKey="example-1-bep-srp-plot" />(c). The <strong>Axis Type</strong> can be
      set to <em>Linear</em>, <em>Logarithmic</em>, <em>Normal Probability</em>, or <em>Gumbel Probability</em> in the <strong>Axis Type</strong> drop-down menu within 
      the <strong>Properties</strong> window, <FigReference figKey="example-1-bep-srp-plot"/>(d), along with other axis customizations.
    </>
  ),
  freeform: ( 
    <> 
      <Figure figKey="example-1-bep-srp-plot"
        caption="Backward erosion piping with intervention system response curve and axis options."
        docId="03-example-1-hazards.mdx" 
        src="figures/desktop-applications/rmc-totalrisk/applications-guide/v1.0/figures/figure7.png" 
        fullWidth={true}
        alt="Backward erosion piping with intervention system response curve and axis options." 
      />
    </> 
  )
}, 
]}

/>

Consequences

Life Loss Function

For this example, daytime and nighttime life loss estimates were developed for a range of reservoir stages for both non-breach and breach scenarios. The daytime exposure scenario rate was assumed to be 45% while the nighttime exposure rate was assumed to be 55%. Three consequence functions are created in RMC-TotalRisk: Day, Night, and Composite. The composite curves are created using the day and night scenarios weighted by their respective exposure rates.

<ProcessList items={[ { //Step 1 title: ( <> Right-click on the Consequences folder in the Project Explorer window and select Add Tabular Consequence… Name the consequence function in the prompt (e.g., Non-Breach_Day) and press OK. </> ) }, { //Step 2 title: ( <> For Hazard Type and Hazard Units, select Stage and ft. For Consequence and Consequence Unit, select Life Loss and Lives, (a). </> ) }, { //Step 3 title: ( <> The Interpolation Transforms are set to None (linear interpolation) for both the Hazard and Consequences, (b). </> ) }, { //Step 4 title: ( <> Select an appropriate input distribution and enter the life loss data into the consequence function. Uncertainty in the life loss values for this project is defined by minimum, most likely, and maximum values for both the daytime and nighttime scenario, . For this dataset, a PERT distribution is selected from the Distribution drop-down. Enter the stage and daytime life loss values from by copying and pasting into the table as indicated in (c). </> ), freeform: ( <> {/Table 4/} <TableVertical tableKey="example-1-non-breach-life-loss" caption="Non-breach life loss." headerAlign={["center", "center", "center", "center", "center", "center", "center", "center", "center"]} headers={[ [ { value: "Stage (ft)", colSpan: 1, rowSpan: 2 }, { value: "Day Life Loss", colSpan: 3, rowSpan: 1 }, { value: "Night Life Loss", colSpan: 3, rowSpan: 1 } ], [ { value: "Minimum"}, { value: "Most Likely"}, { value: "Maximum"}, { value: "Minimum"}, { value: "Most Likely"}, { value: "Maximum"} ] ]} columns={[ [ //Stage (ft) '641.00', '642.50', '644.50', '647.00', 649.65, '653.00', '656.00' ], [ //DLL Minimum 0, 0, 0, 5, 15, 35, 75 ], [ //DLL Most Likely 0, 0, 0, 25, 45, 80, 160 ], [ //DLL Maximum 0, 0, 0, 55, 80, 170, 275 ], [ //NLL Minimum 0, 0, 0, 10, 25, 50, 95 ], [ //NLL Most Likely 0, 0, 0, 40, 60, 90, 185 ], [ //NLL Maximum 0, 0, 0, 65, 90, 160, 300 ] ]} alt="A table documenting the non-breach life loss for the daytime and nighttime scenario." /> {/Figure 8/}

</> ) }, { //Step 5 title: ( <> Repeat the same process to create a non-breach life loss consequence function for the nighttime scenario. Enter the stage and nighttime life loss values from by copying and pasting into the table as indicated in . </> ), freeform: ( <> </> ) }, { //Step 6 title: ( <> Right-click on the Consequences folder in the Project Explorer window and select Add Composite Consequence… Name the consequence function in the prompt (e.g., Non-Breach) and press OK. </> ) }, { //Step 7 title: ( <> For Hazard Type and Hazard Units, select Stage and ft. For Consequence and Consequence Unit, select Life Loss and Lives, (a). </> ) }, { //Step 8 title: ( <> The Interpolation Transforms are set to None (linear interpolation) for both the Hazard and Consequences, (b). </> ) }, { //Step 9 title: ( <> Since pre-defined weights will be used to combine the daytime and nighttime scenarios, the Composite Type within the Consequence Functions section of the Properties window is set to Mixture. To add consequence functions to the composite consequence function, click the Add row(s) to the bottom of the table button. The Non-Breach_Day and Non-Breach_Night functions are selected from the drop-down menu, and the appropriate weights are assigned to each function to create the composite, (c). </> ) }, { //Step 10 title: ( <> To keep the Project Explorer window organized, multiple functions of the same type can be grouped together. Select the Non-Breach_Day, Non-Breach_Night, and Non-Breach consequence functions by holding down the Shift key and selecting them. Right-click and select Group. Name or rename the group as desired, (d). </> ), freeform: ( <> </> ) }, { //Step 11 title: ( <> Follow the same procedure outlined in Steps 1 through 10 to create the consequence functions for an internal erosion breach using the data in . BEP is an internal erosion mechanism, and internal erosion failure modes were assumed to have the same consequences in this example. The internal erosion breach composite function is shown in . </> ), freeform: ( <> {/Table 5/} <TableVertical tableKey="example-1-internal-erosion-breach-life-loss" caption="Internal erosion breach life loss." headerAlign={["center", "center", "center", "center", "center", "center", "center", "center", "center"]} headers={[ [ { value: "Stage (ft)", colSpan: 1, rowSpan: 2 }, { value: "Day Life Loss", colSpan: 3, rowSpan: 1 }, { value: "Night Life Loss", colSpan: 3, rowSpan: 1 } ], [ { value: "Minimum"}, { value: "Most Likely"}, { value: "Maximum"}, { value: "Minimum"}, { value: "Most Likely"}, { value: "Maximum"} ] ]} columns={[ [ //Stage (ft) '641.00', '642.50', '644.50', '647.00', 649.65 ], [ //DLL Minimum 75, 95, 86, 103, 121 ], [ //DLL Most Likely 125, 170, 152, 176, 216 ], [ //DLL Maximum 180, 245, 228, 259, 344 ], [ //NLL Minimum 90, 125, 114, 118, 145 ], [ //NLL Most Likely 165, 195, 179, 194, 251 ], [ //NLL Maximum 220, 275, 252, 290, 326 ] ]} alt="Internal erosion breach life loss for the daytime and nighttime scenario." /> {/Figure 11/} </> ) } ]} />

Economic Cost

To create an economic cost consequence function, the procedure is the same as documented in Life Loss Function. In step 2 and step 7, the Consequence and Consequence Unit should be set to Economic Cost and $, respectively. No economic costs were modeled for this example.

Risk Analyses

Once all necessary components have been added, a risk analysis is created using the following procedure. For this example, there is only one risk analysis required to compute the life safety risk associated with the BEP failure mode. Had economic costs been modeled, a separate risk analysis would have been necessary to compute the economic risk for the failure mode.

<ProcessList items={[ { //Step 1 title: ( <> Right-click the Risk Analyses folder and select Add Risk Analysis… Name the risk analysis in the prompt (e.g., Backward Erosion Piping with Intervention) and press OK. </> ) }, { //Step 2 title: ( <> For Consequence and Consequence Unit in the Risk Analysis Properties section of the Properties window, select Life Loss and Lives, (a). </> ) }, { //Step 3 title: ( <> For this risk analysis one hazard function, one system response function, and two consequence functions are required, (b). Add components to the risk analysis Diagram by clicking the green plus sign, clicking on a node output connector, or right-clicking anywhere in the diagram. </> ), child: [ { //Step 3a title: ( <> First, add a hazard node to the diagram. Select the hazard function (e.g., Stage Frequency) from the blank drop-down box in the hazard node. </> ) }, { //Step 3b title: ( <> Next, add the non-breach condition by clicking on the hazard node output connector and adding a consequence node and selecting the composite non-breach life loss function (e.g., Non-Breach) from the drop-down box. </> ) }, { //Step 3c title: ( <> Finally, add the backward erosion piping potential failure mode and the associated breach condition. </> ), child: [ { //Step 3c.i title: ( <> Add a response node by clicking on the hazard node output connector and select the appropriate system response function (e.g., Backward Erosion Piping with Intervention) from the drop-down box. </> ) }, { //Step 3c.ii title: ( <> Add the breach condition by clicking on the response node output connector and adding a consequence node and selecting the composite breach life loss function (e.g., Internal Erosion) from the drop-down box. </> ) } ] }, { //Step 3d title: ( <> Re-arrange the nodes (click and hold, then drag) as desired to personalize the diagram. </> ) } ] }, { //Step 4 title: ( <> When running a risk analysis with uncertainty, the simulation options can be adjusted within the Options tab of the Properties window. </> ), child: [ { //Step 4a title:( <> Within the Simulation Options section, the Confidence Interval is set to 90% and Realizations is set to 10,000, (a). </> ) }, { //Step 4b title:( <> The Integration Options, System Component Options, System Options, and Risk Measure Options are set to their default values, (b). </> ) } ] }, { //Step 5 title: ( <> To run the risk analysis without uncertainty, select Simulate Mean Risk Only in the Simulation section of the Properties window and click Estimate, (c). To run the risk analysis with uncertainty, select Simulate Risk with Full Uncertainty. </> ), freeform: ( <> {/Figure 12/}

{/Figure 13/} </> )
} ]} />

Results

Once the risk analysis model has been simulated, the Summary Statistics tab provides a table of summary results. The Risk Types reported in RMC-TotalRisk are Incremental, Background, Total, Failure, and Non-Failure. For this example, the incremental Mean, E[N] (also referred to as the average annual life loss, AALL), of 1.11E-03 and an Exceedance Probability, α (also referred to as annual probability of failure, APF) of 7.02E-06 were calculated for BEP with intervention.

The F-N Plot is viewed by clicking on the F-N Plot tab within the risk analysis window. The F-N Plot displays the probability distribution of life loss from all potential failure modes and all population exposure scenarios for each inundation scenario. Incremental, background (non-breach), and total (residual) risk can be portrayed on this plot as shown in Error! Reference source not found. The F-N Plot can also portray uncertainty in the risk analysis results. shows the incremental risk F-N plot for this example with uncertainty.

The α-ƞ Plot (also commonly referred to as the f-N̅ Plot) is viewed by clicking on the α-ƞ Plot tab within the risk analysis window. The α-ƞ Plot displays the annual probability of failure and weighted average life loss with uncertainty, .

{/Figure 14/}

{/*Figure 15*/} {/*Figure 16*/}