y=kx-a y=the time per cycle k=the time for the first cycle x=the number of cycles a=a constant representing the learning curve percentage
Let?s take an example to see how this works. A certain task takes 50 minutes the first time it is done. The second time it takes 40 minutes. The fourth time it takes 32 minutes. Each time the number of cycles is doubled, the time to complete the task is .8 of the time. This would then be called an 80% learning curve.
Using the above equation we can solve for the variable a for the 80% learning curve:
a=(log k - log y)/log x
Using a simple case of second cycle and y=10 this simplifies to:
a=(log 10 - log 8)/log 2
=.322
using the first equation we can verify our time for the 4th cycle:
y=50 x 4-.322
=32
So there you have all the math required to use learning curves.
