Improved Mean and Variance Estimating Formulas for PERT Analyses

Abstract

The program evaluation and review technique (PERT) is a popular method for measuring and controlling activity progress in projects. Its structure is simple, and the result is fairly accurate as long as none of its base assumptions is violated. Many authors have challenged these assumptions and suggested improvements to the mean and variance formulas. This paper quantifies the accuracy of a wide range of PERT mean-variance estimation formulas. In addition, we develop a new PERT variant using common percentiles. The proposed method uses three points for estimation, just like the classical PERT. However, it provides options for the selection of the three points. It provides different set of probability weights by the selection of the three points and what parameter to estimate, i.e., mean or variance, which minimizes the estimation error. We compare the accuracy of our approach with existing methods using the Pearson distribution system. Our use of the Pearson system allows us to systematically compare different PERT methods over a wider range of distribution shapes than has previously been considered. This analysis shows that, despite its simple structure, our new method outperforms existing methods when estimating means and variances of most bell-shaped and J-shaped beta distributions. We also demonstrate how practitioners could use our new methods in actual project settings.