A dynamic model f or PERT risk evaluating in fuzzy environment

n this paper we propose a dynamic model for evaluating of time risk in stochastic network, where the activity durations are exponentionaly distributed random variable and independent. We would like to present a new definition of general risk index for project in each time and connect it to the notation of its activity criticalities. We model such networks as finite-state, absorbing, and continuous Marko chain with upper triangular generator matrices. The state space is related to the network structure. The criticality index for each activity will be computed and then we put forward a fuzzy way of measuring the criticality to computing project states criticality. Then by using the probability of absorption in each state severity of criticality will be computed dynamically. The criticality measure obtained may serve as a measure of risk or of the supervision effort needed by senior management. It also by ranking the states before project initiating is able to forecast the critical states in order and help to the project management to developing a proper guideline for resource planning and allocation.