Technical Note—A Method for Combining Three-Valued Predictions

This note shows a method for finding readily the distribution of the sum or product of variables for which predictions are available in three-valued form: a most likely value together with high and low values that each have specified probabilities of occurrence. It is assumed that the variables have a Weibull distribution. Using dimensionless graphs entered with an “asymmetry quotient” found arithmetically from the original prediction values, the first, second, and third moments of each Weibull distribution are found. Then the moments of the individual distributions are combined to find the three moments of the overall distribution. If desired, these combined moments can be converted to the three-value form of the original estimates—a low, most likely, and high figure. The method described can be used instead of Monte Carlo methods, avoids their possible uncertainties, and does not require a computer. It is generally more accurate than another alternative, the approximations used in summing PERT critical paths.