Abstract
An earlier paper presented a method for using response times to construct a PERT network representing the mental activities in a task. A key role in this method is played by parameters called coupled slacks. The magnitudes of the coupled slacks are used to test the validity of a PERT model and to deduce aspects of the structure of the network. In a stochastic PERT network, the usual estimate of coupled slack based on the mean completion times can be biased. Distribution-free upper and lower bounds are derived for the bias, and it is shown that the bias approaches zero as the probability of relatively long prolongations increases. It is also shown that the expected value of the estimate of coupled slack between two activities is negative only if the two activities are in a Wheatstone bridge. Finally, an estimate of the increase in completion time due to prolonging an activity, given that the prolongation did in fact increase the completion time, is derived.
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