A Note on the Measurement of Cost/Quantity Relationships in the Aircraft Industry

Many practical applications of learning theory in the aircraft industry require the estimation of the parameters of y_i = αiβ where y_t is the cost of the i^th aircraft. Typically data are available by production lot rather than by individual aircraft. The estimation procedure usually employed is the application of least squares to log y_v = log α = β log x_v where y_v is the mean cost of a production lot and x_v is a quantity “near” the mean of serial numbers of the craft. This note presents a probability model which leads directly to maximum likelihood estimators and avoids difficulties inherent in the usual approach. An example of estimation employing methods of non-linear estimation is presented.