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Interconnected Estimating Relationships: Their Derivation and Application

Applications Track



By the term “Interconnected Estimating Relationships”, we mean estimating relationships for hardware and software costs, schedules, weights, and below-the-line programmatic costs that are jointly impacted by each other or by the same drivers. There are two common examples of this phenomenon: (1) cost-estimating relationships and schedule-estimating relationships, which are interconnected for many reasons, but primarily because a projects schedule is a significant driver of its cost; and (2) cost-estimating relationships for hardware and software and techniques for estimating below-the-line costs, the latter of which is typically done by applying a factor or percentage to the hardware and/or software cost estimate. A critical consideration in all of these estimating relationships is the fact the results of such estimates, due to influences of risk and uncertainty, cannot be expressed as single numbers, but rather must be reported as probability distributions. As R.P. Covert (Journal of Cost Analysis and Parametrics, Spring 2008) observed, not only are cost and schedule estimates uncertain, but the same is true for cost and schedule drivers, such as weight, power, and lines of code. It follows that the drivers are themselves better expressed as probability distributions. A situation that more clearly illustrates the fact that a cost or schedule drivers should really be modeled as a probability distributions is the case of so-called “cost-on-cost” CERs, where a below-the-line cost, e.g., system engineering, is estimated as a factor times the cost estimate (not times the cost, because we don’t know the cost – all we know is the estimate). A cost-on-cost CER is really a “cost-estimate-on-cost-estimate” CER, because the driver, namely hardware and/or software cost, is itself the result of an estimating relationship. That estimating relationship drives the system engineering cost through the estimating relationship Y = aX, where Y is system-engineering cost and X is hardware and/or software cost. This presentation offers the statistical foundations of working with interconnected estimating relationships and provides an example of how they operate in practice to give us a better understanding of project costs and schedules.


Stephen A. Book
Dr. Stephen A. Book recently vacated the position of Chief Technical Officer of MCR, LLC to concentrate on research and training. In his former capacity, he was responsible for ensuring technical excellence of MCR 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. Earlier, at The Aerospace Corporation, he was a principal contributor to several Air Force cost studies of national significance, including the DSP/FEWS/BSTS/AWS/Brilliant Eyes Sensor Integration Study (1992) and the ALS/Spacelifter/EELV Launch Options Study (1993). He has served on national panels as an independent reviewer of NASA programs, for example the 2005 Senior External Review Team on cost-estimating methods for the Exploration Systems Mission Directorate, the 1998-99 National Research Council Committee on Space Shuttle Upgrades, and the 1997-98 Cost Assessment and Validation Task Force on the International Space Station (“Chabrow Committee”). 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, The Journal of Cost Analysis and Parametrics. He was the 2005 recipient of ISPA’s Freiman Award for Lifetime Achievement and the 2010 recipient of SCEA’s Award for Lifetime Achievement. Dr. Book earned his Ph.D. in mathematics, with concentration in probability and statistics, at the University of Oregon.

Amanda J. Feather
Amanda J. Feather has a background in mechanical engineering and cost estimating for space programs. Currently located at MCR’s El Segundo CA office, Ms. Feather supports the Air Force Cost Analysis Agency at the USAF Space and Missile Systems Center, Los Angeles, estimating costs and schedules for various space programs. Prior to joining MCR, she worked on national programs and power systems for military communication satellites at Boeing Satellite Systems. Ms. Feather earned her B.S. in Mechanical Engineering, with concentration in manufacturing, at Rensselaer Polytechnic Institute, New York.