Back to the Big Easy: Revisiting Hilbert’s Problems for Cost Estimating

Management Track




At the International Congress of Mathematicians at the Sorbonne in Paris in 1900, German mathematician David Hilbert boldly put forth a list of 23 theretofore unsolved problems in mathematics, which subsequently became quite influential in 20th-century research efforts. At the Joint SCEA/ISPA Conference in New Orleans in June, 2007, the authors audaciously emulated Hilbert with a list of 21 problems for cost estimating and risk analysis. Because cost is an inherently but not purely analytical field, some of the problems took the form of broader issues to be addressed, and because cost is an interdisciplinary field, there’s always a chance some of the problems may have been solved elsewhere (such as in the realm of probability and statistics) but the solution not yet fully “imported” into the cost world. This paper is a progress report of sorts, summarizing much of the research that has occurred in the intervening six years, and adding in a few new problems we neglected to include the first time because our proverbial headlights did not shine far enough down the cost estimating highway.

The original problems were grouped into four categories. The first, Professional Identity, comprised the body of knowledge, community of practice, analyst paradox, and integrity of the profession. Developments here include the merger of ISPA and SCEA to form ICEAA; the rebirth of CostPROF as CEBoK, and designation of the Body of Knowledge (BoK) Chair distinct from Training; the publishing of the GAO Cost Estimating and Assessment Guide; the establishment of the OSD CAPE by WSARA, subsuming the erstwhile Cost Analysis Improvement Group (CAIG); and the continued reinvigoration of the profession by bright young analysts as the Baby Boomers draw ever nearer to retirement.

The second category, Analytical Techniques, comprised double analogy, theoretical probabilistic underpinnings, standardization of CERs, thought experiments, grand unified theories, or GUTs, of learning curve and estimates at complete (EACs), physics-based estimating, and estimating emerging technology. Developments here include numerous papers on risk, general-error regression models (GERM), serious concerns with the traditional Cumulative Average (CUMAV) learning curve formulation, progress-based EACs, and new trends in software and automated information systems (AIS), including enterprise resource planning (ERP). Other technological advances likely remain buried in the black world.

The third category, Cost Estimating Implementation, comprised meta-cost estimating, data rights management, epistemology of cost models, and blended cost models. There has been perhaps the least progress here, though developments such as XML-based CPRs, IMS-based cost models, and conflation of multiple probabilistic estimates show some promise. The fourth category, Integration with Related Disciplines, comprised “self-fulfilling prophecy,” skewness in risk, portfolio management, contract incentives, and the uncertain partnership with cost management. Developments here include the infamous 80th percentile of WSARA and its retraction, research into heteroskedastic regression models for the size effect, extensions of risk-based return on sales (ROS), and the Better Buying Power initiatives. A combination of the debt crisis, pending sequestration, and the end of the Iraq and Afghan wars promises to spur renewed interest in portfolio management for the DoD.

While the original list of problems was surprisingly relevant and comprehensive, a few major areas were not anticipated. One is the emergence of joint cost and schedule risk analysis; the related interest of cost estimators in schedules, as evidenced by GAO’s “sequel” Schedule Assessment Guide; and the coincident improvements in Monte Carlo simulation technology. Other key risk analysis areas include the enhanced scenario-based method (eSBM), the use of SME assessments, and data-based coefficients of variation (CVs) and correlations.


Peter J. Braxton
Technomics, Inc.
Peter J. Braxton is a Senior Cost Analyst and Technical Officer at Technomics, Inc., where he supports the Naval Center for Cost Analysis (NCCA) on data collection and cost research efforts, and Defense Acquisition University (DAU) on curriculum development.
He is a Certified Cost Estimator/Analyst (CCEA) and currently serves as Body of Knowledge Chair for the the International Cost Estimating and Analysis Association (ICEAA). He was named the Society of Cost Estimating and Analysis (SCEA) 2007 Estimator of the Year for contributions in Education. He is the managing editor for development and maintenance of the acclaimed Cost Estimating Body of Knowledge (CEBoK(R)) and its predecessor, Cost Programmed Review Of Fundamentals (CostPROF). He served as SCEA’s Training Chair from 2004 to 2009 and as Training Track chair for nine consecutive SCEA international conferences. He has taught extensively at government, corporate, and society training events throughout the United States, Europe, and Australia.
He holds an AB in Mathematics from Princeton University and an M.S. in Applied Science (Operations Research) from the College of William and Mary. He is lead author or co-author of over two dozen professional papers on cost, risk, and Cost As an Independent Variable (CAIV), including three SCEA Best Paper winners and a Journal of Cost Analysis and Parametrics article.

Richard Coleman