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Robust Default Correlation for Cost Risk Analysis

Risk II Track




Correlation is an important consideration in cost risk analysis. Exclusion of correlation from cost risk analysis results in the de facto assumption that all risks are independent. The assumption of independence leads to significant underestimation of total risk. However, figuring out the correct correlation values between work breakdown structures elements can be challenging. For instance, it is difficult to estimate the exact correlation value between the structures and thermal protection subsystems in a cost risk estimate.

In order to circumvent these issues a default correlation value is often used. A commonly used value, attributed to Dr. Steve Book, is 20%. There is some empirical evidence to support this value. The basis for the 20% is discussed, and the supporting empirical evidence is presented. However, this evidence is limited, and the default value is sensitive to error in the assumption. For example, in a 100-element work breakdown structure, if the true correlation is 60%, the risk, as measured by the total standard deviation of the estimate, is underestimated by 40%. A new approach to default correlation is presented that minimizes the total error when the assumed correlation is not equal to the actual correlation. This approach is robust in the sense that the error is minimized. Depending upon the underlying assumption, this value varies significantly. The pros and cons of each assumption are discussed, and a new recommended default value is proposed. The derivation of the values is presented in detail.


Christian Smart
Missile Defense Agency
Dr. Christian Smart is employed as the director for cost estimating and analysis at the Missile Defense Agency (MDA). In this capacity, he is responsible for overseeing all cost estimating activities developed and produced by the agency, and leads a 100- person team. Prior to joining MDA, Dr. Smart worked as a senior parametric cost analyst and program manager with Science Applications International Corporation. An experienced estimator and analyst, he was responsible for risk analysis and cost integration for NASA’s Ares launch vehicles. Dr. Smart spent several years overseeing improvements and updates to the NASA/Air Force Cost Model and has developed numerous cost models and techniques that are used by Goddard Space Flight Center, Marshall Space Flight Center, and NASA HQ. In 2010, he received an Exceptional Public Service Medal from NASA for his contributions to the Ares I Joint Cost Schedule Confidence Level Analysis and his support for the Human Space Flight Review Panel led by Norm Augustine. He has given numerous presentations on cost modeling and risk analysis both in the U.S. and abroad. He was awarded best of conference paper at the 2008 Annual Joint ISPA-SCEA conference in Noordwijk for “The Fractal Geometry of Cost Risk,” best of conference paper at the 2009 Annual Joint ISPA-SCEA conference in St. Louis for “The Portfolio Effect and the Free Lunch” and best of conference paper at the 2010 Annual Joint ISPA-SCEA conference in San Diego for “Here, There Be Dragons: Considering the Right Tail in Risk Management.” Dr. Smart was named the 2009 Parametrician of the Year by ISPA. He is a SCEA certified cost estimator/analyst (CCEA), a member of the Society for Cost Estimating and Analysis (SCEA) and the International Society of Parametric Analysts (ISPA). Dr. Smart is a past president of the Greater Alabama Chapter of SCEA, is the managing editor for The Journal of Cost Analysis and Parametrics, and serves as the Region III VP on the SCEA national board of directors. Dr. Smart earned bachelors degrees in Economics and Mathematics from Jacksonville State University, and a Ph.D. in Applied Mathematics from the University of Alabama in Huntsville.