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Statistical Foundations of Adaptive Cost-Estimating Relationships

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, e.g., components, subsystems or entire systems of satellites, ground systems, etc. In this paper, we review an extension of the concept of “analogy estimating” to parametric estimating, namely the concept of “adaptive” CERs – CERs that are based on specific knowledge of individual data points that may be more relevant to a particular estimating problem than would the full data set. The goal of adaptive CER development is to be able to apply CERs that have smaller estimating error and narrower prediction bounds. Several examples of adaptive CERs were provided in a paper presented by the first two authors to the July 2008 ISPA/SCEA Conference held in Industry Hills CA.

This presentation focuses on statistical foundations of the derivation of adaptive CERs, namely the method of weighted least-squares (WLS) regression. Ordinary least-squares (OLS) regression has been traditionally applied to historical-cost data in order to derive additive-error CERs valid over an entire data range, subject to the requirement that all data points are weighted equally and have residuals that are distributed according to a common normal distribution. The idea behind adaptive CERs, however, is that data points should be deweighted based on some function of their distance from the point at which an estimate is to be made, i.e., each historical data point should be assigned a “weight” that reflects its importance to the particular estimation that is to be made using the derived CER. This presentation describes technical details of the WLS derivation process, resulting quality metrics, and role played in adaptive-CER development.


Stephen A. 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 working in the System Planning and Engineering Group. 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. Other work included support of the BSS Design Center’s Integrated Engineering Laboratory with the creation of several automated cost tools, which uses a spacecraft’s system-level set of parameters to generate costs. 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. He earned an M.S. in Economics, specializing in econometrics from the University of Southern California.

Daniel I. 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.