1

When estimating activity durations, you get a duration plus/minus a sigma (standard deviation) for each activity.

Afterwards, when you want to determine the critical path, what figure should you use for the duration of each activity?

Or, how should you include the plus/minus of the standard deviation in the activity duration?

2

I think there are a couple of misconceptions in this question - at least from the way I learned the topics.

First, estimating the duration of activities is not done with an duration +/- sigma. Sigma would only have meaning if the estimate were computed as an average of multiple independent estimates. While this may be feasible in some situations, I'm skeptical that it is used very often. I believe the more common duration estimate is to use a PERT methodology. PERT involves a most likely estimate, an optimistic estimate and a worst case estimate. The most likely estimate is multiplied by 4, then the worst case and best case are added and the resulting sum is divided by 6 to get the estimate of record. That estimate (O+P+(4ML))/6 is used as the estimated duration of each activity.

The second misconception is that critical path cannot be calculated for each activity estimate; critical path is an emergent property of the project schedule, not a property of any individual activity. The critical path is the set of activities that determine the minimum length of the project.

Having dispensed with those two issues, I believe what you're looking for is a way of modelling the critical path that incorporates the uncertainty of duration estimates. The standard method to model & understand the uncertainty of a set of semi-independent activities is the Monte Carlo method. Monte Carlo is not for the faint of heart, and the full value of the Monte Carlo method relies on an understanding of the distribution of the estimates and some other math underpinnings. I haven't reviewed it, but a colleague recommended this link as a simple yet effective discussion of Monte Carlo.

My apologies if I've made flawed assumptions about the nature of your question.

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