A simple and logical alternative for making PERT time estimates

The two standard steps for estimating PERT times are: Step 1, estimate a, m, and b; and Step 2, use the 'classical' formulae mu = (a + 4m + b)/6 and sigma = (b - a)/6. We review the shortcomings of the textbook definitions of a, m and b; we also review the inconsistency of Step 1 with the literature on probability elicitation. A 5- or 7-fractile alternative is then proposed and justified for Step 1. Next, we develop simple but very accurate formulae for computing mu and sigma with the fractiles estimated in our Step 1. For contrast, we also show that the classical PERT formulae are very inaccurate, even for the very restricted subset of beta distributions for which the formulae are supposedly applicable. Our overall purpose is to combine earlier findings with some new results to argue that: (i) the classical PERT formulae are both illogical and inaccurate, so we should not continue to teach and use them; and (ii) simple and more logical alternatives are available.