Estimation problems in rate-augmented learning curves

In situations where production rate is variable, the learning curve can provide unreliable results. One proposed solution to the "production rate" problem is to multiplicatively augment the learning curve with a production rate explanatory variable, while widely used by cost analysts, the rate-augmented learning curve has not proved reliable. It has been assumed, but not demonstrated, that data and measurement problems lead to unreliable parameter estimates. In this paper we demonstrate that the parameter estimates are a function of the units in which the cost and delivery data are measured; hence, the estimates are always arbitrary. We propose a procedure for obtaining meaningful estimates, but it requires assigning weights to the cost and delivery time data. We use a simple dynamic program to demonstrate that proper estimates of sign and magnitude can only be obtained when the learning and rate equations are estimated simultaneously and the sum-of-squares for the rate equation receives a higher weighting in the estimation. These results have major implications for cost analysts. Since accurate parameter estimation requires weighting, estimation by unweighted ordinary least squares is a futile effort.