Time Phasing Aircraft R&D Using the Weibull and Beta Distributions

Abstract

Early research on time phasing primarily focuses on the theoretical foundation for applying the cumulative distribution function, or S-curve, to model the distribution of development expenditures. Minimal methodology prior to 2002 provides for estimating the S-curve’s parameter values. Brown et al. (2002) resolved this shortcoming through regression analysis, but their methodology is not specific to aircraft and does not consider aircraft-specific variables, such as first flight. Using a sample of 26 Department of Defense aircraft programs, we build upon Brown et al.’s work by examining whether a model driven by aircraft-specific variables can more accurately predict budget requirements. As a baseline, we compare our model to the commonly cited 60/40 “rule of thumb,” which assumes 60% expenditures at 50% schedule. We discover that our developed Weibull model explains 74.6% of total variation in annual budget, improving the estimation of budgets by 6.5%, on average, over the baseline 60/40 model.

Notes

1. The use of the 60/40 heuristic is not unique to aircraft only, as the NASA Cost Estimating Guide (2002) references the 60/40 S-curve as a “rule of thumb” for spreading space expenditures.

2. Lee et al. (1996) trace the source of the 60/40 heuristic to an undocumented circa-1980 OSD-CAIG research effort titled Military Aircraft Development Cost Study, as recalled by Mr. Gary Christle, USD(AT&T)/API.

3. We exclude the C-17A from our regression models for two reasons. First, the C-17A consistently resulted in Cook’s D values above 0.5, which indicates that a data point is significantly influential on the linear regression model estimates (Neter, Kutner, Nachtsheim, and Wasserman, 1996, p. 380). Second, a qualitative review of acquisition history reveals that the C-17A suffered extensive development delays due to contracting difficulties, budget cuts, and management problems, as evidenced by a 1990 USAF Inspector General investigation alleging management improprieties (Saxer, 1995). Although schedule delays are not uncommon for aircraft development, we determine that the extent of the C-17A’s delays make it a unique data point.

Additional information

Notes on contributors

Gregory E. Brown

Gregory E. Brown is a cost analyst at the Air Force Life Cycle Management Center, Wright-Patterson Air Force Base, Ohio.

Edward D. White

Dr. Edward D. White is a Professor of Statistics in the Department of Mathematics and Statistics at the Air Force Institute of Technology. His primary research interests include statistical modeling, simulation, and data analytics.

Jonathan D. Ritschel

Dr. Jonathan D. Ritschel is an Assistant Professor of Cost Analysis at the Air Force Institute of Technology. His research interests include public choice, institutional analysis, and cost analysis.

Michael J. Seibel

Michael J. Seibel is a senior cost analyst at the Air Force Life Cycle Management Center, Wright-Patterson Air Force Base, Ohio.