#### Comparing Different Methods for Deriving Cost-Dependent CERs

**Models Track**

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#### Abstract:

Parametric cost estimating relationships (CER) are developed using historical data. Regression analysis is used to determine whether the independent variables can help explain the variation in the dependent variable. There are two different types of independent variables in CERs: technical parameters (e.g., weight, power, etc.) and cost-dependent parameters (e.g., first unit production cost, Prime Mission Product [PMP] cost, etc.). When CERs are generated, they are based upon actual data from completed projects whether or not the independent variables are cost- dependent or hardware design-driven.

Although CERs are developed in parallel using the “actual” data set, they may be used in series in cost uncertainty analysis, especially when the aggregated costs are used as independent variables. For example, let us consider the System Engineering and Program Management (SEPM) cost as a function of the PMP cost. The SEPM cost can be estimated only after the PMP cost is derived by the cost model (through another CER or a series of CERs). Since we use the “CER- estimated” (not actual) PMP to predict SEPM when analyzing cost uncertainties, the estimate and variance for SEPM as well as total cost will be inaccurate if the SEPM CER is built using the “actual” cost. In other words, this two-step process introduces error into the independent variable PMP, which is further compounded with the error of estimating SEPM cost and the total project cost. Reference 1 suggests using an alternative approach to avoid these errors: develop the SEPM CER using the “estimated” PMP cost instead of the “actual” PMP cost.

This paper will first examine whether this alternative method makes sense from a statistician’s perspective. A mathematical proof is provided. We will then apply this alternative method to analyze the SEPM and integration, assembly, and test (IA&T) CERs in the Unmanned Space Vehicle Cost Model, Eighth Edition (USCM8) database. The USCM8 CERs were developed using the Minimum-Unbiased-Percentage Error (MUPE) method to model multiplicative errors. The MUPE method is also known as an iterative, weighted least squares (WLS) regression. The goal of this paper is to compare the cost-dependent CERs generated by the current (based on actual data) and the alternative methods to determine whether there are any significant differences. It will also compare their respective standard percent errors (SPE).

#### Author:

**Dr. Shu-Ping Hu**

Chief Statistician at Tecolote Research, Inc. Dr. Hu joined Tecolote in 1984 and serves as a company expert in all statistical matters. She has over 15 years of experience supporting Unmanned Space Vehicle Cost Model (USCM) CER development and the related database. She also has 21 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 many major cost conferences, advocating the most advanced cost analysis techniques, and earning several best paper awards. She earned her Ph.D. in Mathematics, with an emphasis in Statistics, at the University of California, Santa Barbara.