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Federal Highway Administration Research and Technology
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Federal Highway Administration > Publications > Public Roads > Vol. 69 · No. 3 > Applying LCCA to Bridges(caption) 
Nov/Dec 2005 

Publication Number: FHWAHRT05001 

Applying LCCA to Bridges(caption)Simulation results for a pavement design showing variation and magnitude of possible outcomes. The charts were developed using the RealCost software and show identical information in both frequency distribution and cumulative probability curves to aid in identifying critical factors. These two charts (on the left) of output frequency distribution show two alternatives that have approximately similar statistical mean values of $3.12 million and $3.18 million, which are the distributions' expected values equivalent to the deterministic values evaluated, making it difficult to discern a meaningful difference without showing the distributions. The shape of the distributions shows that one alternative has less variation from its mean than the other. The cumulative probability chart on the right shows the same information in a different format: the percent chance, or probability, of the cost having a value less than or equal to a certain cost value on the horizontal axis based on the risk assumptions used in the analysis. This probability is equal to the portion of area under the distribution curve from the left limit to that cost value. The total area under each distribution curve is equal to 1.0, and in the cumulative probability curve the probability of having a cost value less than or equal to the largest cost value is equal to 1.0. The analyst can note that the alternative with less variation from the mean has a steeper cumulative probability curve than the other due to the concentration (less variation) of the area around the mean in the distribution curve. For example, it is unlikely that the cost in the alternative with a steep cumulative curve will be less than or equal to $3.08 million, while there is a 40percent chance that the cost in the other alternative will be less than or equal to $3.08 million. Where the two lines cross, the analyst would note that 84 percent of the time, either alternative would cost $3.21 million or less. This bar graph shows the cost components of the projects to be scheduled in the years 2005, 2015, 2025, 2035, and 2045, in addition to the annual costs and the residual values in 2054 for the 12 alternatives. The horizontal axis represents the year and the alternatives grouped by year. The vertical axis represents the LCC components in millions of dollars for each alternative in each year in which the project is scheduled. 
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