Learning Curve Tool

This tool performs a quick learning curve calculation. Given the theoretical first unit cost (in dollarss), the total quantity of units to be produced, and the learning curve slope (LCS), the calculator returns the cumulative average unit cost for the lot and the cost of the Nth unit (where N = X). The learning curve slope is the percentage decrease in cost experienced every time X doubles. Therefore the LCS must be a value between 0 and 1 in order to get correct output. Note that the calculator goes to two decimal places, so if the LCS is extremely low, it is possible to get a 'Nth unit cost' of $0.

Inputs

    
T1 ($) = T1 is the theoretical 1st unit cost
X = X is the total quantity of units to be built
LCS = LCS is the Learning Curve Slope with 0 < LCS < 1
 


Outputs

    
Cum Avg Unit Cost = This is the average unit cost for the lot of X units
Nth Unit Cost = This is the cost of the Nth unit
 


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S Curve Tool

This tool generates a yearly outlay profile for a specified program budget. The outlay, in this instance, is generated by the cumulative distribution function (CDF) for the Weibull distribution. The formula for the Weibull CDF is

Weibull

where 't' = time in years, 'alpha' is the scaling parameter, and 'beta' is the shape parameter. A few illustrative examples are provided so the user can graphically see the output for several alpha and beta combinations. The x-axis is time (showing 0 to 10 years) and the y-axis is f(t) on a scale from 0 to 1. Note that depending upon the alpha and beta values, a yearly profile outlay could extend for a relatively short duration (3 years for alpha = 4, beta = 2) or a longer duration (greater than 10 years for alpha = 0.5, beta = 2).

alpha beta Corresponding Outlay Profile
0.5 2 S curve5
1 2 S curve6
2 2 S curve7
4 2 S curve8
0.5 4 S curve4
1 4 S curve3
2 4 S curve
4 4 S curve2

While the illustrative examples give an idea of how the Weibull distribution is used to generate potential outlay profiles, it is useful to see how well the process can approximate real world data. The table below presents the "Outlay Rates to be Used for Incremental Changes in BA Purchases" from Table 5-11 of the National Defense Budget Estimates for FY2012. For each line of data in the table, the 'best fit' alpha and beta values were derived using the least squares methodology. The user can take those 'best fit' alpha and beta values, use them as input for the S Curve Tool, and see how closely the Tool output matches the FY12 outlay rates.

  FY12 Outlay Rates*   'Best Fit' Derivations
Category Yr1 Yr2 Yr3 Yr4 Yr5 Yr6   alpha beta
Military Personnel    
Army 0.753 0.198 0.050         1.087 0.739
Navy 0.883 0.100 0.018         0.894 0.427
Marine Corps 0.809 0.145 0.046         0.881 0.569
Air Force 0.836 0.138 0.026         0.991 0.553
Operation & Maintenance    
Army 0.376 0.540 0.037 0.019 0.017 0.012   2.560 1.314
Navy 0.532 0.385 0.047 0.021 0.016     1.814 1.147
Marine Corps 0.306 0.538 0.083 0.052 0.009 0.012   2.448 1.457
Air Force 0.458 0.457 0.041 0.025 0.009 0.010   2.159 1.231
Procurement    
Army Aircraft 0.110 0.400 0.298 0.150 0.022 0.020   2.301 2.307
Army Missiles 0.083 0.420 0.325 0.140 0.020 0.012   2.525 2.282
Navy Aircraft 0.150 0.400 0.286 0.100 0.045 0.019   2.170 2.184
Navy Weapons 0.220 0.320 0.270 0.120 0.035 0.035   1.726 2.284
Air Force Aircraft 0.070 0.400 0.280 0.140 0.080 0.030   2.255 2.396
Air Force Missiles 0.300 0.310 0.250 0.080 0.038 0.022   1.496 2.038
RDT&E    
Army 0.010 0.355 0.280 0.230 0.100 0.025   2.343 2.805
Navy 0.050 0.455 0.300 0.150 0.030 0.015   2.566 2.242
Air Force 0.050 0.408 0.330 0.160 0.032 0.020   2.569 2.376
* Source: National Defense Budget Estimates for FY2012

The S Curve Tool has three input fields: Budget ($M), alpha, and beta. The Tool spreads the Budgeted amount across the years based upon the Weibull CDF function and the values that the user inserts for the alpha and beta parameters. In addition to the yearly outlay profile, the output also includes the CDF value and the "% of the Total Budget" for each year. To give an example of how the 'Best Fit' Derivations can be tested, consider the Military Personnel - Army in the first row. Regardless of what the user inputs for the Budget, inputting alpha = 1.087 and beta = 0.739 should lead to the CDF and "% of Total Budget" fields in the output approximating the values in the FY12 Outlay Rates columns. It is left to the user to do the comparison.

Inputs

    
Budget ($M) = The budgeted amount for the program
alpha = Alpha is the scaling parameter (length of program)
beta = Beta is the shape parameter (when peak expenditure year occurs)
 


Outputs

      
 
CDF
% of Total
Budget ($M)
Yr 1
Yr 2
Yr 3
Yr 4
Yr 5
Yr 6
Yr 7
Yr 8
Yr 9
Yr 10
 

Note that the output values are all rounded. That is why a "% of Total" value may appear as '0' while the Budget ($M) has a value in it. Also, the approximations sometimes have "tails" that extend substantially beyond the exact FY12 Outlay Rates, but they are usually very small dollar amounts.

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Inflation Tool

This tool performs a quick inflation calculation. Given the base year dollar value, the assumed inflation rate, and the number of years to which the rate gets applied, the resulting out year dollar value is provided. The inflation multiplication factor is shown as well.

Inputs

    
Base Year Dollar Value = Dollar value in year 0
Yearly Inflation Rate= Assumed yearly inflation (e.g. 5% should be entered as 1.05)
Number of Years = Years of inflation
 


Outputs

    
Inflation Mult Factor = This is multiplied by the Base Year value to get the Out Year value
Out Year Dollar Value = Dollar value after the years of inflation