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A Non-Simulation Based Method for Inducing Pearson’s Correlation Between Input Random Variables

Methods & Models Track

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Several previously published papers have cited the need to include correlation in risk analysis models. In particular, a landmark paper published by Philip Lurie and Matthew Goldberg presented a methodology for inducing Pearson’s correlation between input/independent random variables. The one subject absent from the paper was a methodology for finding the optimal applied correlation matrix given a desired outcome correlation. Since the publishing of the Lurie-Goldberg paper there has been continuing discussion on its implementation, however there has not been any presentation of an optimization algorithm that does not involve the use of computing-heavy simulations.
This paper reviews the general methodology used by Lurie and Goldberg (along with its predecessor papers) and presents a non-simulation approach to finding the optimal input correlation matrix given a set of marginal distributions and a desired correlation matrix.


Eric Druker
Eric R. Druker graduated from the College of William and Mary with a B.S. in Applied Mathematics in 2005 concentrating in both Operations Research and Probability & Statistics with a minor in Economics. He is employed by Northrop Grumman as a Technical & Research lead. He performs cost and risk analysis on several programs within both the Intelligence and DoD communities. He was a recipient of the 2005 NGIT President’s award for his work on Independent Cost Evaluations during which he helped to develop the risk process currently used by NGIT’s ICE teams. As a member of Northrop Grumman’s ICE working group, he has helped shape the cost and risk practices used on independent cost estimates and evaluations across the corporation. In addition to SCEA conferences, Eric has also presented papers at the Naval Postgraduate School’s Acquisition Research Symposium, DoDCAS and the NASA PM Challenge. He has also performed decision tree analysis for NG Corporate law and built models for Hurricane Katrina Impact Studies and Schedule/Cost Growth determination.

Richard Coleman
Richard L. Coleman is a 1968 Naval Academy graduate, received an M. S. with Distinction from the U. S. Naval Postgraduate School and retired from active duty as a Captain, USN, in 1993. His service included tours as Commanding Officer of USS Dewey (DDG 45), and as Director, Naval Center for Cost Analysis. He has worked extensively in cost, CAIV, and risk for the Missile Defence Agency (MDA), Navy ARO, the intelligence community, NAVAIR, and the DD(X) Design Agent team. He has supported numerous ship programs including DD(X), the DDG 51 class, Deepwater, LHD 8 and LHA 6, the LPD 17 class, Virginia class submarines, CNN 77, and CVN 21. He is the Director of the Cost and Price Analysis Center of Excellence and conducts Independent Cost Evaluations on Northrop Grumman programs. He has more than 65 professional papers to his credit, including five ISPA/SCEA and SCEA Best Paper Awards and two ADoDCAS Outstanding Contributed Papers. He was a senior reviewer for all the SCEA CostPROF modules and lead author of the Risk Module. He has served as Regional and National Vice President of SCEA and is currently a Board Member.

Peter Braxton
Peter J. Braxton 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 has worked to advance the state of knowledge of cost estimating, Cost As an Independent Variable (CAIV), Target Costing, and risk analysis on behalf of the Navy Acquisition Reform Office (ARO), the DD(X) development program, and other ship and intelligence community programs. He has co-authored several professional papers, including ISPA/SCEA International Conference award-winners in CAIV (1999) and Management (2005). He served as managing editor for the original development of the acclaimed Cost Programmed Review Of Fundamentals (CostPROF) body of knowledge and training course materials and is currently undertaking to lead a large team of cost professional in a comprehensive update thereof. He serves as SCEA’s Director of Training, a Northrop Grumman Technical Fellow, and Director of Research within TASC’s Management Consulting Division. He was named SCEA’s 2007 Estimator of the Year for contributions in Education.

Joel Hughes
Joel B. Hughes received a B.S. in Finance from the University of South Alabama, along with an M.B.A from Tennessee Technological University. He is also beginning work towards an M.S. in Operations Management at the University of Alabama. Currently working as a Senior Business Analyst, he has performed cost and risk analysis on several programs at Northrop Grumman Ship Systems sector. He is the recipient of multiple Business Management Awards, and was instrumental in initializing the risk quantification process at Ship Systems.