For a PERT network, a new method is developed for estimating the criticality index of activity i (ACI(i)) as a function of the expected duration of activity i (mu(i)) and for the sensitivity analysis of the expected project completion time (mu(T)) with respect to mu(i). The proposed method evaluates the frequency of activity i being on the critical path, and thereby its ACI(i) using Monte Carlo simulation or a Taguchi orthogonal array experiment at several values of pi, fits a logistic regression model for estimating ACI(i) as a function of mu(i), and then, using the estimated ACI(i) function, evaluates the amount of change in mu(T)-when mu(i) is changed by a given amount. Unlike the previous works, the proposed method models ACI(i) as a nonlinear (ie, logistic) function of mu(i), which can be used to estimate the amount of change in mu(T) for a variety of changes in mu(i). Computational results indicate that the performance of the proposed method is comparable to that of direct Monte Carlo simulation. Journal of the Operational Research Society (2004).