Statistical Foundations of Adaptive Cost-Estimating Relationships

Traditional development of cost-estimating relationships (CERs) has been based on “full” data sets consisting of all available cost and technical data associated with a particular class of products of interest, e.g., components, subsystems or entire systems of satellites, ground systems, etc. In this article, we review an extension of the concept of “analogy estimating” to parametric estimating, namely the concept of “adaptive” CERs—CERs that are based on specific knowledge of individual data points that may be more relevant to a particular estimating problem than would the full data set. The goal of adaptive CER development is to be able to apply CERs that have smaller estimating error and narrower prediction bounds. Several examples of adaptive CERs were provided in a presentation (Book & Broder, 2008) by the first two authors to the May 2008 SSCAG Meeting in Noordwijk, Holland, and the June 2008 SCEA/ISPA Conference in Industry Hills, CA. This article focuses on statistical foundations of the derivation of adaptive CERs, namely, the method of weighted least-squares regression. Ordinary least-squares regression has been traditionally applied to historical-cost data in order to derive additive-error CERs valid over an entire data range, subject to the requirement that all data points be weighted equally and have residuals that are distributed according to a common normal distribution. The idea behind adaptive CERs, however, is that data points should be “deweighted” based on some function of their distance from the point at which an estimate is to be made. This means that each historical data point should be assigned a “weight” that reflects its importance to the particular estimation that is to be made using the derived CER. This presentation describes technical details of the weighted least-squares derivation process, resulting quality metrics, and the roles it plays in adaptive-CER development.