## Question

I just am having trouble trying to calculate a learning curve and quantity curve equation. I was provided an average unit price and a total lot quantity procured in FY18 and I'm trying to adjust my FY19 estimate with a 95% quantity curve and a 95% learning curve. Somehow I just keep getting the math wrong and now my head is spinning. I can provide you with my excel formula if you would like. Any help is appreciated.## Answer

Open full Question DetailsYou are missing one piece of critical information: You need to know the

unit numbers as the items came off the production line in FY18.

In particular, you'll want to know the unit number of the first unit produced in 2018, and,

the last unit number produced in 2018.

You'll also want to know all previous year cost and lotsize information.

If you can't find the FY2017 and earlier data, then you're stuck with only the FY18 data. You can "work up" the LC to find a T1, but this would be modeling where you'd be forced into using the 95% learning and 95 rate assumptions. Which the data (if you had it) would help you determined the actual learning and rate affect acheived. You can do senstiivity analysis on each of teh learning and rate curve percentage assumptions.

Note, this methodology allows the data collected from the last lot to be EXTREMELY influential in your cost estimate. You'd be much better served if you can find other actuals (from previous lots) and do analysis (non linear regression or MUPE or Ridge Regression or analogy) to find estimates for the parameters of the learning curve with rate model (A, b, and c).

You should ask yourself, "are the cost data (average cost of FY19 units), the 95% Learning and the 95% production rate accurate?" The sensitivity analysis on those values will show much a small change in one of those parameters inpacts your estimate.

With the unit numbersof the FY18 lot, you'd compute the ALM of the FY18 lot

(ALM = (First + Last+2 *sqrt(First*Last))/4).

Let's say that the number that you've computed, the ALM, is a number called Z. By definition the cost of unit number Z is the average cost of the units

built in FY18. Cost of Unit Z is YunitZ=LotAUCFY18 Now, you can solve for A, in the equation, YunitZ = A * Z^ b * Q^c ,

since, YunitZ, Z, b, Q, and c are all known values (Q is the number of units in the FY18 lot).

Rearranging: A = YunitZ /( Z^ b * Q^c).

Now, that you know A, go back to your estimate for future lots in future

years, and use the following model: Y=A*(x^b)*(Q^c)

Where, this is the model equation for learning curve with rate described below.

Let A = your T1 (theoretical cost of your first unit)

Let b = the learning curve exponent which in your example is log base 2 of 0.95 or LN(.95)/LN(2)

Let c = the rate curve exponent which in your example is log base 2 of 0.95 or LN(.95)/LN(2)

The learning curve with production rate formula is

Where Y =cost of some unit x built with a production rate of Q

So, if your FY19 lot consists of units 101-140 build with an annualized production rate of 40 per year,

Then the cost of units in the FY19 lot are

Y101 = A * 101^ b * 40^c

Y102 = A* 102^b * 40^c

Y103 = A* 103^b * 40^c

. . .

. . .

. . .

Y140 = A* 140^b * 40^c

I refer you to the Cost Analyst Spreadsheet Toolbox found on the DAU website, here:

https://www.dau.mil/tools/t/Cost-Analyst-Spreadsheet-Tool-box

document.title = "Ask a Professor: Calculate a learning curve and quantity curve equation";