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RealCost User Manual

Entering, Saving, and Loading Data

Simulation and Outputs

The Simulation and Outputs section of the Switchboard is where deterministic life-cycle costs and simulations of probabilistic life-cycle costs are performed. Deterministic analysis is done using either deterministic inputs or most likely values for probabilistic inputs; in either case, point values are used in a deterministic analysis.

Deterministic Results

Opening the Deterministic Results form, shown in Figure 21, calculates deterministic present values for both agency and user costs and displays those values. The lowest cost alternatives for both agency and user are labeled. The form also provides a direct link to the Deterministic Results Excel worksheet, which contains all of the information required to investigate deterministic results.

Figure 21. Deterministic Results form.
Figure 21. Deterministic Results form. Deterministic Results form. The total present value cost results in thousands of dollars are displayed for two alternatives. For Alternative 1: Hot Mix Asphalt, the agency cost is $5,909.73 (thousands) and the user cost is $21,450.11 (thousands). For Alternative 2: Stone Matrix Asphalt, the agency cost is $6,026.59 (thousands) and the user cost is $18,764.58 (thousands). The form displays the lowest present value agency cost as Alternative 1: Hot Mix Asphalt and the lowest present value user cost as Alternative 2: Stone Matrix Asphalt. The command buttons Go to Worksheet and Close appear at the bottom of the form.

Probabilistic Analysis

Running the Simulation

Running a simulation is a necessary step toward performing a probabilistic analysis. To conduct probabilistic analysis, RealCost uses Monte Carlo simulation, which allows modeling of uncertain quantities in the model with probabilistic inputs. The simulation procedure randomly samples these inputs and produces outputs that are described by both a range of potential values and a likelihood of occurrence of specific outputs. The simulation produces the probabilistic outputs; without running a simulation, probabilistic outputs are not available. The Simulation form is shown in Figure 22.

The Sampling Scheme section of the form determines from where the software will draw its simulation numbers. Choosing Random Results causes the simulation seed value (where the simulation starts) to come from the computer's internal clock. While not truly random, this seed value cannot be influenced by the software user, and it produces different values with each simulation.

Figure 22. Simulation form.
Figure 22. Simulation form. Simulation form. The form has three sections: Sampling Scheme, Iteration, and Tail Analysis Percentiles. Sampling Scheme fields allow the choice of Random Results or Reproducible Results (in the sample form, Reproducible Results is checked). When Reproducible Results is chosen, the Seed Value data entry field allows entry of a value. In this example, 2000 is entered as the seed value. Data entry fields in the Iteration section are Number of Iterations with a value of 2000 and a Monitor Convergence checkbox that is unchecked; the Monitoring Frequency (Number Iterations) and Convergence Tolerance (%) fields, have values of 50 and 2.5 that show in gray because Monitor Convergence is not checked. The Tail Analysis Percentiles section shows four fields and values: Percentile 1 is 5, Percentile 2 is 10, Percentile 3 is 90, and Percentile 4 is 95. The command buttons Simulate and Close appear at the bottom of the form.

The value of choosing Reproducible Results is that the analyst may perform separate simulation runs to compare more than two alternatives. "Reproducible Results" causes the same simulation values for each given seed value. Using reproducible results causes the same random numbers to be generated. This removes random variability associated with the seed value from the comparison, allowing the analyst to focus on actual input changes.

The Sampling Scheme section of the form determines how the software will draw its simulation numbers from the pseudo-random number generator (these numbers are not truly random but are satisfactory for simulation purposes). Choosing Random Results causes the simulation to start the random number sequence from a "seed" value taken from the computer's internal clock. This seed value cannot be influenced by the software user and produces different values with each simulation.

The Reproducible Results option allows the analyst to specify the specific seed value to be used in all simulations. This causes the same set of random numbers to be generated from the pseudo-random number generator. Choosing Reproducible Results allows the analyst to perform separate simulation runs to compare multiple alternatives, knowing that variations from run to run will be caused by actual input changes and not variability associated with different seed values.

Tail Analysis Percentiles are used to conduct analysis on the total cost probability distribution graphics provided by RealCost, discussed on page 44. Percentile values should be entered in ascending order.

The Iteration section is used to determine the number of iterations to be performed and whether the simulation will be monitored for convergence. Output convergence can be used by the analyst to determine that a simulation has run a sufficient number of iterations to properly define its outputs. Convergence is monitored by comparing the change in the mean and standard deviation of the cumulative outputs each time a specified number of iterations is completed (specified in the Monitoring Frequency box). Once the level of change falls below the specified Convergence Tolerance, RealCost will end the simulation run without completing any remaining iterations-yielding probabilistic results while significantly shortening the time it takes to complete the analysis. The number of iterations should be 2,000 at a minimum. Monitoring Frequency is adequate at 100 iterations, and, when used, a Convergence Tolerance of 2.5 (percent) should provide appropriate probabilistic outputs.

Figure 23 shows a simulation that ended due to simulation convergence of less than 2.5 percent. Note that the convergence error is listed at the bottom of the form. This convergence error is monitored and reported during the simulation.

Figure 23. Simulation form at the conclusion of a simulation run.
Figure 23. Simulation form at the conclusion of a simulation run. Simulation form at the conclusion of a simulation run. The Simulation form and data that are described in Figure 22 are shown again with these changes: The 'Monitor Convergence' checkbox is checked; the value of 50 in the Monitoring Frequency field and the value of 2.5 percent in the Convergence Tolerance field are no longer grayed out. Below the fields, the results of the simulation appear: Converged after 750 Iterations, Final Error = 1.56%, and Simulation Time = 621.99 seconds.

Analyzing Probabilistic Results

After a simulation run, probabilistic results are available for analysis. A simulation must be run prior to viewing probabilistic results. Figure 24 shows the results of a probabilistic simulation.

Figure 24. Probabilistic Results form.
Figure 24. Probabilistic Results form. Probabilistic Results form. The form displays the total present value cost results for two alternatives in table format. The table has five columns. The first column names the four values displayed: Mean, Standard Deviation, Minimum, and Maximum. The second and third columns display the four values for Alternative 1 Agency Cost and Alternative 1 User Cost in thousands of dollars. The fourth and fifth columns display Alternative 2 Agency Cost and User Cost in thousands of dollars. Command buttons at the bottom of the form are Probabilistic Results Worksheet, Output Distributions Worksheet, Tornado Graphs Analysis Worksheet, Extreme Tail Analysis Worksheet, and Close.

Four worksheets are accessible from the Probabilistic Results form. The Probabilistic Results worksheet and the Output Distributions worksheet both provide probability distribution and cumulative density functions that describe outputs. Examples of these graphs are shown in Figure 25.

Figure 25. Probabilistic distribution density and cumulative density functions describing outputs.
Figure 25. Probabilistic distribution density and cumulative density functions describing outputs. Probabilistic distribution density and cumulative density functions describing outputs. The sample line graph shows the probability curves and the cumulative density curves of two different alternatives.

The Tornado Graphs worksheet provides tornado graphs that describe how inputs affect outputs (example shown in Figure 26). For example, the input Initial Construction Cost has a significant effect on the output Alternative 1: Agency Costs. A correlation coefficient value of 1 would indicate a complete positive correlation between two variables. A value of -1 would indicate a complete inverse correlation between two variables. The value of 0 would indicate that there is no correlation between variables: they are independent. Other correlation values indicate a partial correlation; the output is affected by changes in the selected input, but may be affected by other variables as well.

Figure 26. Correlation coefficient graph (aka "tornado graph").
Figure 26. Correlation coefficient graph (aka "tornado graph"). Correlation coefficient graph (aka 'tornado graph'). The sample bar graph shows the correlation coefficient outputs for Alternative 1 Agency Cost input variables. The results are Initial Construction Cost 0.85, Initial Construction Life, -0.33, Discount Rate -0.29, Rehab 1 Life -0.24, Rehab 1 Cost 0.14, Rehab 2 Life -0.14, and Rehab 2 Cost 0.13.

Total Cost Probability Distributions

While the correlation coefficient graphics describe the sensitivity of outputs to individual inputs, the total cost probability distribution graphics provided by RealCost describe the sensitivity of outputs to combinations of inputs. Particular emphasis is given to the tails of the distribution, which encompass the most extreme outcomes encountered in the analysis. The analyst may enter four Tail Analysis Percentiles (see Figure 22, Simulation form) to define the areas of the tails of most interest. RealCost demonstrates how various inputs act together to produce these four defined tail areas.

For example, Figure 27 shows an agency project alternative total cost distribution. The shaded area on the left side of the distribution curve represents a 10 percent tail of the area under the curve (the 10th percentile, or the most favorable 10 percent of all agency cost outputs). Table 8 describes the combination of input values that would lead to that outcome. The values under the "10%" heading represent the number of standard deviations from the mean value for each of the inputs needed to fall within the 10 percent tail.

Figure 27. Tail analysis outputs.
Figure 27. Tail analysis outputs. Tail Analysis outputs. In the bell-shaped curve of a project alternative's total cost distribution, a shaded area on the left side represents the most favorable 10 percent of all agency cost outputs, that is, the 10 percent tail.

Table 8. Most favorable 10 percent of expected agency cost outcomes.
Input Variable Name Alternative 1: Agency Cost
5% 10% 90% 95%
Discount Rate 0.56 0.74 -0.79 -1.02
Initial Construction Cost -1.76 -1.44 1.36 1.41
Initial Construction Life 0.65 0.57 -0.54 -0.81
Rehab 1 Life 0.86 0.54 -0.37 -0.46

The value of tail analysis is that it identifies those inputs that contribute to the success, or failure, of a project alternative. Pavement design decisionmakers are able to quantitatively identify alternatives that they believe they are able to positively influence and also those alternatives that they are not able to influence. More discussion on interpreting probabilistic outputs is given in FHWA's LCCA Technical Bulletin, Life-Cycle Cost Analysis in Pavement Design (FHWA-SA-98-079).

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Updated: 10/23/2013