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Accuracy Matters: Selecting a Lot-Based Cost Improvement Curve

Methods and Models I Track




There are two commonly used cost improvement curve (CIC) theories: unit cost (UC) theory and cumulative average cost (CAC) theory. Ideally, analysts develop the CIC by analyzing unit cost data. However, it is common that instead of unit costs, analysts must develop the CIC from lot cost data. An essential step in this process is to estimate the theoretical lot midpoints (LMP) for each lot, to proceed with the curve-fitting process. LMP is generally associated with UC theory, where the midpoint is always within the lot. The more general lot plot point (LPP) term is used in the context of both the UC and CAC theories.

Many research papers have been published on CICs, including several that discuss estimating the LMP. A two-term formula has traditionally been used as a useful approximation to derive the lot total cost (LTC), as well as the LMP under UC theory (see SCEA CEBoK, Module 7 [Reference 1]). There is, however, a more accurate six-term formula to better approximate the LTC and LMP. This increase in accuracy may be substantial for high-cost items or an aggregated estimate, consisting of many CIC-related items. The more accurate formula can also impact cost uncertainty analysis results, especially when thousands of iterations are performed.

This paper describes how to derive and use LPPs for both the UC and CAC theories. We describe how the analyst can use LPPs to construct prediction intervals (PI) for cost uncertainty analysis. This approach is more efficient and appropriate than using the UC curve directly. In addition, this paper will (1) detail an iterative, two-step regression method to implement the six-term formula, (2) describe the advantages of generating the LPPs for CICs, (3) recommend an iterative (not direct) approach to fit a CIC under cumulative average theory, and (4) compare CICs derived using the two-step regression method with CICs generated by the simultaneous minimization process. Different error term assumptions and realistic examples are also discussed.


Shu-Ping Hu
Tecolote Research, Inc.
Dr. Shu-Ping Hu is Chief Statistician at Tecolote Research, Inc. Dr. Hu 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. At Tecolote, she has published many technical papers, covering such topics as developing the PING Factor to adjust log-linear CER results to reflect the mean in unit space and suggesting an adjusted R-square measure for the Minimum-Unbiased-Percentage-Error (MUPE) CER. She has 20 years of experience supporting Unmanned Space Vehicle Cost Model (USCM) CER development and the related database. She also has 24 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 at major cost conferences, and has received several best paper awards for presenting the most advanced cost analysis techniques.

Alfred Smith
Tecolote Research, Inc.
Mr. 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 spent a total of 21 years in the Canadian Navy serving in positions such as submarine navigator, operations officer and as a naval architect. 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 military, Coast Guard, NASA and foreign projects. He has been with Tecolote since 1995 and since 2000 has been the General Manager for Tecolote’s Software Products/Services Group, responsible for the development, distribution and support of a variety of web and desktop tools supporting the cost community.