Time Calculation for Project Activities

Expected Times for Activities
For each activity in the project network, not only is an estimate made of the most probable time required to complete the activity, but some measure of uncertainty is also noted in the estimate. The pessimistic estimate and optimistic estimate is also made to have an idea of the approximate maximum and minimum completion times respectively for the activity.

PERT calculates the expected value of activity duration (te) as a weighted average of the three time estimates. The expected time is the best estimate that we can make of the time required for a single occurrence of an activity.

Variability of Activity Times
One measure of variability of possible activity times is given by the standard deviation of their probability distribution. Standard deviation and variance are commonly used as measures of variability among numbers. The variance (Vt) is simply the average squared difference of all the numbers from the mean value. The standard deviation (St) is the square root of the variance.

The Expected Length of a Critical Path
The expected length of a sequence of independent activities is simply the sum of their separate expected lengths. We calculate a te for every activity in the project network and use these te s to identify the critical path. We obtain an expected length of the project (Te) by summing the expected activity durations along the critical path.
Similarly, the variance (VT) of a sum of independent activities is equal to the sum of their individual variances and the standard deviation of the project length (ST) is the square root of VT.

Effects of Near-Critical Path
We calculate Te by adding the te s of the critical path activities. But it might not always be the best estimate of project length because under some combination of activity times and variances, a near-critical path may exist with a higher variance than the "main" critical path. Thus, where the possibility of uncertain activity times is admitted, the possibility of alternate critical paths is implied and the simple estimating procedures tend to yield overly optimistic results.

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