Stochastic PERT networks as models of cognition: Derivation of the mean, variance, and distribution of reaction time using Order-of-Processing (OP) diagrams

Abstract

It is frequently assumed that the mental activity which leads to a given response is made up of separable components or processes. One or more of the processes are assumed to contribute to the time required to respond. Computation of the mean, variance, and distribution of the reaction time is relatively straightforward when all processes are arranged in series or parallel. However, such is not the case when the processes have complex arrangements. A solution to a useful special case of the above problem is proposed. Specifically, it is shown that simple computations yield closed form expressions for the mean, variance, and distribution of reaction time when the processes can be arranged in a stochastic PERT network and when the durations of individual processes are sums of mutually independent, exponentially distributed random variables. The method of solution relies on the construction of an Order-of-Processing (OP) diagram from the original PERT network representation of behavior.