Bounding the Project Completion Time Distribution in PERT Networks

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Abstract
We consider the PERT model of a project composed of activities whose durations are random variables with known distributions. For the situations in which the activity durations are completely independent, we present a new method for obtaining a probability distribution function that bounds the exact probability distribution of the project completion time from below. The bounding distribution can be used to obtain an upper bound on the mean completion time of the project. We also prove and illustrate that this bounding distribution is better (tighter) than any of the existing lower bounds, implying that the corresponding upper bound on the mean completion time is tighter than any of the existing upper bounds.