Date of Award


Document Type


Degree Name

Master of Science


Department of Mathematics and Statistics

First Advisor

Edward D. White, PhD


Norden (1970) uses the Rayleigh, which is a degenerative of the Weibull, to model manpower on research and development (R&D) programs. Several research efforts extend his work including Lee, Hogue, and Gallagher (1997) who build R&D 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 R&D defense programs, we develop regression models to predict the requisite shape and scale parameters to forecast Weibull-based budgets. Using the remaining 26 completed R&D 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 R&D 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.

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