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Modeling Deterioration Over Time

The hyperbolic function can be used to approximate a wide variety of age-efficiency patterns, and those with a β greater than zero are concave in shape (See Decay Functions figure above). A concave hyperbolic function is used to model assets that lose little productive capacity during the early stages of their service lives (i.e., slow decay of efficiency) but experience rapid loss of productive capacity toward the end of their service lives. A β of zero creates a linear decay function, which is appropriate for assets that depreciate at a constant rate over their lifetime.  A hyperbolic function was assumed to best simulate deterioration for all Corps mission areas. For this study, β is assumed to be 0.6 for the Flood Risk Management, Multipurpose, and MR&T functional categories. This value is approximately the midpoint between 0.5 and 0.75, the range recommended by OECD (2009). The β for the Navigation functional category is assumed to be 0.5, the range minimum, due to its unique lifecycle characteristics that are heavily impacted by sedimentation, requiring periodic dredging to extend overall asset service life.

A β of zero was used to simulate the linear deterioration associated with sedimentation and dredging process over all navigation projects throughout USACE.

This study estimates a 75-year service life assumption for the Navigation functional category and a 60-year service life assumption for all other functional categories excluding Dredging. Dredging projects have a much shorter service life compared to other functional categories. a 15-year service life was chosen for the Dredging functional category. Dredging-related capital improvements have a shorter lifespan than more durable assets such as dams and levees.

The figure to the right shows the applied decay functions for each of the defined USACE functional categories.  The table below shows the decay functions and parameters used for each functional category.

Graphic of Mission Area Decay Functions

Decay Functions and Parameters

Mission Area Decay Function Decay Constant Assumed Service Life
Flood Risk Management Hyperbolic 0.6 60
Navigation  Hyperbolic 0.5 75
Navigation Dredging Linear 0 15
Multipurpose Hyperbolic 0.6 60
Mississippi River & Tributaries Hyperbolic 0.6 60
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