PERT and the beta distribution

After reviewing the beta distribution and its properties, a simple technique is described for obtaining exact solutions to the cubic equation which results from the PERT constraint on standard deviation. These solutions are then used, together with the expression for the mode of the beta distribution, to determine graphically the specific values of the parameters of a beta distribution which may be associated with any particular set of PERT estimates. Expressions are derived for approximate values of these parameters in terms of the PERT estimates explicitly, and a comparison is made of the exact and approximate values. The PERT approximation concerning expected time is examined and confirmed to be an excellent simple approximation for the exact value of the associated beta distribution. It is concluded that the beta distributions associated with PERT are not necessarily as restricted, and the differences between the PERT values of expected time and standard deviation and the exact values for the associated beta distribution are not as great, as has previously been indicated in the literature.