Improved modeling of three-point estimates for decision making: going beyond the triangle

Abstract

Decision making in engineering development projects and programs relies on numbers. This quantitative support can involve uncertainty that is frequently characterized by three-point estimates of decision variables. Modeling of these estimates for analysis commonly utilizes the triangular distribution for its simplicity, but errors could be introduced if another distribution model is more appropriate for the data. This study measures statistics from distribution types ranging from fully flat to narrowly peaked, fitting estimates for all sizes of minimum to maximum ranges and spanning the complete spectrum of asymmetry. The study compares common statistical values for each distribution to an equivalent triangular distribution. It calculates the error size for the mean, high-confidence interval, and coefficient of variation. The study then provides recommendations for when to use a triangular distribution or a different model. The guidelines are based on a weight factor of the distribution mode and the estimate’s maturity to produce an objective set of guidelines for selecting distribution shapes best suited to model any given three-point estimate. With these guidelines, estimators and modelers can quickly and easily provide a more accurate uncertainty analysis to support decision makers.