Int. J. Production Economics 62 (1999) 219}232 On the sensitivity of project variability to activity mean duration S.E. Elmaghraby*, Y. Fathi, M.R. Taner Graduate Program in Operations Research, North Carolina State University, Box 7913, Raleigh NC 27695-7913, USA Received 23 June 1998; accepted 29 September 1998 Abstract Traditionally the &importance' of an activity in the PERT model of projects is measured by its &criticality index', which is de"ned as the probability that the activity will be on the longest path. An insightful discussion by Williams (1992, Journal of Operational Research Society 43, 353}357) revealed that the classical criticality index is not always informative or intuitively appealing. In a recent study by Cho and Yum (1997, International Journal of Production Research 35, 2737}2757), a new &Uncertainty Importance Measure' is de"ned to measure the e!ect of the variability in an activity duration on the variability of the overall project duration. They propose Taguchi's sampling technique as a method for analyzing the network. The main contribution of this paper is to study the impact of changing the mean duration of an activity on the variability of the project duration. On the way to accomplish this, we further investigate the accuracy of Taguchi's sampling method for approximating the mean and standard deviation of the project duration, and propose steps that could result in computational savings in large networks.  1999 Elsevier Science B.V. All rights reserved. Keywords: Activity networks; Taguchi sampling; Sensitivity analysis 1. Introduction We consider an activity network (AN) with random activity durations (the PERT model), and address the following problem: What is the impact of a change in the time to process an activity on the project comple- tion time? In particular, we are concerned with the impact of changes in the mean duration of an activ- ity on the variance of the project duration. There is a vast literature dealing with the issues of estimating some network parameters, such as the * Corresponding author. Tel.: # 1 919 515 7077; fax: # 1 919 515 5281; e-mail: elmaghra@eos.ncsu.edu. distribution function, or the "rst few moments (especially the mean and variance) of the time of realization of nodes,  and in particular the terminal node since it signi"es the completion of the project; see the paper of Elmaghraby [1] for a review. A related problem that has also received some attention is concerned with measuring the &import- ance' of an activity relative to other activities, as well as relative to the completion time of the project, which we shall denote by B  . The concept  We assume throughout the activity-on-arc (AOA) repres- entation, with start node 1 and terminal node n. 0925-5273/99/$ - see front matter  1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 5 2 7 3 ( 9 8 ) 0 0 2 4 1 - 2