# An empirical analysis of stochastic PERT networks with gamma parameters

## Date

## Authors

## Journal Title

## Journal ISSN

## Volume Title

## Publisher

## Abstract

The objective of this research is to develop a procedure to analyze PERT networks whose activity times follow a gamma distribution. The advantage of using a gamma distribution to describe a PERT activity time lies in its requirement of only two time estimates and in the provision for an error probability on one of these estimates. A procedure is developed to assign a unique gamma distribution to each activity time. At the network level, the conventional PERT procedure employs the approximate beta means of the activity times to obtain the expected project completion time. The variance of the project completion time is obtained as the sum of the variances of the activities along the critical path of the deterministic network. Such a procedure results in an under-estimation of the expected completion time and a wrong estimation of the variance of the completion time. The difficulty in assigning a unique beta distribution to each activity time makes simulation of PERT networks infeasible. The use of a gamma distribution in PERT networks makes simulation of the network an easy procedure. An analytical procedure is also developed to obtain an approximate distribution of the project completion time. This procedure uses series and parallel reductions to replace a module of activities at each stage by a single activity. Since the series and parallel reductions yield approximate results, an efficient application of the reductions in a network is also discussed with respect to the network configurations. Finally, a procedure is developed to obtain approximate criticality indices of the activities in the network. These indices can be used to select a small set of activities for the purpose of crashing.