Accuracy Matters: Selecting a Lot-Based Cost Improvement Curve

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Accuracy Matters: Selecting a Lot-Based Cost Improvement Curve

Journal of Cost Analysis and Parametrics

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There are two commonly used cost improvement curve theories: unit cost theory and cumulative average cost theory. Ideally, analysts develop the cost improvement curve by analyzing unit cost data. However, it is common that instead of unit costs, analysts must develop the cost improvement curve from lot cost data. An essential step in this process is to estimate the theoretical lot midpoints for each lot, to proceed with the curve-fitting process. Lot midpoints are generally associated with unit cost theory, where the midpoint is always within the lot. The more general lot plot point term is used in the context of both the unit cost and cumulative average cost theories. Many research papers have been published on cost improvement curves, including several that discuss estimating the lot midpoint. A two-term formula has traditionally been used as a useful approximation to derive the lot total cost, as well as the lot midpoint under unit cost theory (see SCEA, 2002–2011; CEBoK, Module 7). There is, however, a more accurate six-term formula to better approximate the lot total cost and lot midpoint. This increase in accuracy may be substantial for high-cost items or an aggregated estimate, consisting of many cost improvement curve-related items. The more accurate formula can also impact cost uncertainty analysis results, especially when thousands of iterations are performed. This article describes how to derive and use lot plot points for both the unit cost and cumulative average cost theories. We describe how the analyst can use lot plot points to construct prediction intervals for cost uncertainty analysis. This approach is more efficient and appropriate than using the unit cost curve directly. In addition, this article will (1) detail an iterative, two-step regression method to implement the six-term formula, (2) describe the advantages of generating the lot plot points for cost improvement curves, (3) recommend an iterative (not direct) approach to fit a cost improvement curve under cumulative average theory, and (4) compare cost improvement curves derived using the two-step regression method with cost improvement curves generated by the simultaneous minimization process. Different error term assumptions and realistic examples are also discussed. In the example section, we show why the goodness-of-fit measures alone should not be used for selecting a best model, especially when either the fit spaces or the dependent variables are different.


Shu-Ping Hu is a Chief Statistician at Tecolote Research, Incorporated. Shu-Ping joined Tecolote in 1984 and serves as a company expert in all statistical matters. She earned her Ph.D. in Mathematics, with an emphasis in Statistics, at the University of California, Santa Barbara. She has published many technical papers, covering such topics as developing the PING Factor to adjust the log-linear CER to reject the mean and suggesting an adjusted R-square measure for the Minimum-Unbiased-Percentage Error (MUPE) and Minimum-Percentage Error Regression under Zero-Percentage Bias (ZMPE) CERs. Dr. Hu has 20 years of experience supporting Unmanned Space Vehicle Cost Model (USCM) CER development and the related database. She also has 25 years of experience designing, developing, and validating statistical, learning, and regression algorithms in CO$TAT. In addition, Dr. Hu developed many of the distribution and correlation algorithms implemented in the ACE RI$K simulation tool. For over 20 years, she has been a regular presenter of the most advanced cost analysis techniques at major cost conferences.

Alfred Smith earned a Bachelor Mechanical Engineering degree from the Canadian Royal Military College and a Master of Science with Distinction in naval architecture from the University College, London, England. He served 21 years in the Canadian Navy in a variety of positions such as submarine Navigator and Operations Officer and then as a naval architect. In addition, he has over 20 years experience leading, executing, or contributing to life cycle cost model development and cost uncertainty analysis for a wide variety of DoD, Coast Guard, NASA, and international projects. Alfred has been employed by Tecolote Research, Inc. since 1995 and became its General Manager for Software Products/Services Group in 2000. His team develops, distributes and supports of a variety of web and desktop products supporting the cost community. Alfred has delivered numerous papers on cost risk analysis topics and was the lead writer of the AFCAA Cost Risk and Uncertainty Handbook. He is certified by ICEAA as a Certified Cost Estimator/Analyst (CCEA®).