For stochastic PERT networks the main difficulty in calculating the probability distribution function (dpf) for project completion time is caused by structural and statistical dependence between activities. This dependency also makes it very hard to identify the most critical paths and activities. This study presents a method for taking into account dependence between activities and provides a generalized algorithm to evaluate the project completion time and criticality index of each activity and path using a Controlled Interval and Memory (CIM) approach proposed by C.B. Chapman and DF. Cooper (1983) Risk engineering: basic controlled interval and memory models. Journal of the Operational Research Society 34(1), 51-60. The procedure allows activity durations to have any continuous or discrete distribution presented in a finite set of ordered pairs. It has been tested using simple activity network models with different statistical and structural dependence between activities. The proposed procedure provides an exact pdf for project completion time when the duration times of activities are discrete and approximates the pdf of the project completion time when the duration times of activities are continuous. Approximation is due to: (i) discretizing continuous distributions, (ii) convoluting discrete approximations to continuous distribution. The computational experience shows that the criticality indices obtained using the proposed procedure is very close to the exact criticality indices obtained using complete enumeration and both methods give the same ranking of criticality indices in most PERT networks. Compared with Monte Carlo simulation, the proposed procedure is comparatively easy to understand and use for simple networks. Moreover, for the same level of precision, Monte Carlo simulation requires much greater computation effort than the proposed procedure. However, Monte Carlo simulation may maintain a comparative advantage for very complex networks, and the ideal approach to networks in general may be a hybrid.