Forecasting Research and Development Program Budgets Using the Weibull Model

Norden (1970) uses the Rayleigh, which is a degenerative of the Weibull, to model manpower on research and development (RD) programs. Several research efforts extend his work including Lee, Hogue, and Gallagher (1997) who build RD program budgets based on Rayleigh expenditures. We demonstrate the theoretical limitations to the Rayleigh model and present the Weibull model, which mitigates those limitations. Using 102 completed RD defense programs, we develop regression models to predict the requisite shape and scale parameters to forecast Weibull-based budgets. Using the remaining 26 completed RD programs to validate the robustness of our regression models, we show that 100 and 96 percent of the least squares estimated shape and scale values respectively, fall within a 95 percent prediction interval. We determine the Weibull model's budget projection capability by comparing forecasted Weibull-based budgets to 128 completed RD program budgets and report an average correlation of 0.607. To determine the significance of our results we compare forecasted Rayleigh-based budgets to the same 128 completed program budgets. Using the Weibull over the Rayleigh model when applying Lee, Hogue, and Gallagher's (1997) methodology, we improve initial budget profile projections on average 60 percent.