If I have a total product made up of several items and subassemblies that each follow a different learning curve but roughly the same quantity, is there a way to derive mathematically the overall learning curve for the sum product of those individual learning curves? I am trying to predict overall product cost (time to manufacture x $/hr) of a product using what is known about the subunits and convert that to a top level learning curve model.
There probably is a way to derive a combination of 2 learning curves. However, if you don't have a Phd in math, the quick and easy way is to use Monte Carlo Simulation. Since you know the parameters of the individual learning curves, you can just plug them into the simulation and let them run. After a sufficient number of interations, you will have an excellent idea of combined learning curve looks like.
Learning curve theory helps you to understand how costs go down over multiple repetitions. When a human being begins to do a repetitive task he will take more time than he will after several repetitions. Since time is money, business owner would like to know what his costs will be over time and repetition.
If you as a business person want to make a bid on a government contract to build 200,000 widgets you would like to know what your total cost is to make the whole production run. If you know the time to make widget one and widget 100, you can calculate the learning curve percentage and thus the time to make each of the widgets in the contract. Is it exact? No, but it is a good approximation. With this information you can make a more exacting bid on your contract. (See Learning Curve Spreadsheet)