Functional estimation of activity criticality indices and sensitivity analysis of expected project completion time

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 (μ _i ) and for the sensitivity analysis of the expected project completion time (μ _T ) with respect to μ _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 μ _i , fits a logistic regression model for estimating ACI _i as a function of μ _i , and then, using the estimated ACI _i function, evaluates the amount of change in μ _T when μ _i is changed by a given amount. Unlike the previous works, the proposed method models ACI _i as a nonlinear (ie, logistic) function of μ _i , which can be used to estimate the amount of change in μ _T for a variety of changes in μ _i . Computational results indicate that the performance of the proposed method is comparable to that of direct Monte Carlo simulation.