Accuracy Matters: Selecting a Lot-Based Cost Improvement Curve

Abstract

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.