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Adaptive Cost-Estimating Relationships

Methods & Models Track

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Traditional development of cost estimating relationships (CERs) has been based on “full” data sets consisting of all available cost and technical data associated with a particular class of Products of Interest (PoIs), e.g., components, subsystems or entire systems of satellites, ground systems, etc. In this paper, we extend the concept of “analogy estimating” to parametric estimating by deriving “adaptive” CERs, namely CERs that are based on specific knowledge of individual data points that may not be reflected in the full data set at the time that the original CER was derived. The goal of adaptive CER development is to be able to apply CERs that have smaller estimating error and narrower prediction bounds.

The paper discusses three general methods of adapting CERs. They are referred to, respectively, as A Priori, Piecewise, and X-Distance. The A Priori method was first discussed in a 1990 paper by the first author (“Deriving Cost-Estimating Relationships Using Weighted Least-Squares Regression”), which examined the general mathematics of applying weights to individual data points supporting CER development by ordinary least squares (OLS) regression. Its focus was on weighting each point by its “quality” or confidence in its accuracy. The second method, Piecewise CER development, calls for grouping the data points into separate subsets based on natural or observable divisions. The third approach weights each data point by a function of its distance from the PoI’s cost-driver value (this is the so-called “X- Distance”). Examples are provided of two separate kinds of weighting functions, an exponential (in particular, a square) and a Gaussian. Examples illustrate the impact of each of these methods on the CERs that can be derived from a sample data set using weighted least squares as the regression technique. Techniques for calculating confidence and prediction intervals are also presented.


Stephen Book
Dr. Stephen A. Book is Chief Technical Officer of MCR, LLC. In that capacity, he is responsible for ensuring technical excellence of MCR’s products, services, and processes by encouraging process improvement, maintaining quality control, and training employees and customers in cost and schedule analysis and associated program-control disciplines. During his career, he has provided technical support in the cost, schedule, and earned-value areas to several Air Force, NASA, and Intelligence organizations and continues to do so. Dr. Book joined MCR in January 2001 after 21 years with The Aerospace Corporation, where he held the title “Distinguished Engineer” during 1996-2000 and served as Director, Resource and Requirements Analysis Department, during 1989-1995. Dr. Book was the last editor of ISPA’s Journal of Parametrics prior to its merger with SCEA’s Journal of Cost Analysis and Management, and is now co-editor of the combined journal. He was the 2005 recipient of ISPA’s Freiman Award for Lifetime Achievement. He earned his Ph.D. in mathematics, with concentration in probability and statistics, at the University of Oregon.

Melvin Broder
Melvin A. Broder is a Senior Project Leader at The Aerospace Corporation. In that capacity he has developed cost models for the Concept Design Center, building and expanding tools for the cost seat and devising new processes. Prior to joining Aerospace he worked in cost estimating at Boeing’s Satellite Systems where he was responsible for front end of the business cost tools and models for Boeing’s commercial product line including support of the BSS Design Center’s Integrated Engineering Laboratory. Mr. Broder has also been a Project Manager for cost tools and processes in the System Engineering Laboratory at Raytheon Systems Company. His responsibilities include the creation and maintenance of tools to support the Sensors and Electronic Systems in design to cost (DTC) and cost-as-an-independent-variable (CAIV) activities. Prior to working the aerospace industry he was an Instructor of Economics at La Verne College, teaching both upper and lower division course work in Micro and Macro Economics, Comparative Economics, Money and Banking, and Econometrics. He earned an M.S. in Economics from the University of Southern California.

Daniel Feldman
Daniel I. Feldman is a Junior Cost Analyst at MCR, LLC. Since joining MCR in early September 2005, he has worked on developing new techniques in utilizing CER-based estimates, along with working on rocket modeling and trade-study analysis. Mr. Feldman earned his B.S. in mathematics in June 2005, with concentration in statistics, at the University of California, Irvine. He is currently working on his M.S. in applied statistics at California State University, Long Beach.