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ANALYTIC AND MONTE CARLO DISTRIBUTION THEORY FOR PERT.
TEXAS A AND M UNIV COLLEGE STATION INST OF STATISTICS
PERT Program Evaluation Review Technique is a method of managing used in planning and control to successfully obtain a stated goal. The fundamental analytic device of PERT is the network, a pictorial arrangement of the work necessary to achieve a given objective, generally the completion of a project. The present PERT analysis replaces the variable completion times in the network by the expected completion time for each activity and computes the critical path as the sequence of activities for which the sum of expected completion times is a maximum. This results in a unique critical path, whereas with the variable completion times the critical path is not always the same. Furthermore, there will be a bias in the estimate of the expected time to complete the project. Hartley and Wortham 1966 have presented integral operators to determine the distribution of the completion time for certain subnetworks and a method of using these operators to reduce the network to an equivalent network with fewer activities. In this dissertation their method will be extended to include other subnetworks and activities whose completion times are not independent. Integral operatiors are presented for the network reductions. The use of these reduction techniques will not, in general, reduce the network to a single equivalent activity, but only to an equivalent network consisting of fewer activities. Methods for estimating the cumulative density function of the project completion time from the reduced network are discussed. A model is also presented which considers dependency among activities in certain types of network configurations.