Statistical AnalysisThe statistical

Statistical AnalysisThe statistical analysis approach requires that activity times be stated in terms of three reasonable time estimates:1. The optimistic time (a) is the shortest time in which an activity can be completed, if all goes exceptionally well.2. The most likely time (m) is the probable time required to perform an activity.3. The pessimistic time (b) is the longest estimated time required to perform an activity.With three time estimates—the optimistic, the most likely, and the pessimistic—the project manager has enough information to estimate the probability that an activity will be completed on schedule. To do so, the project manager must first calculate the mean and variance of a probability distribution for each activity. In PERT/CPM, each activity time is treated as though it were a random variable derived from a beta probability distribution. This distribution can have various shapes, allowing the most likely time estimate (m) to fall anywhere between the pessimistic (b) and optimistic (a) time estimates. The most likely time estimate is the mode of the beta distribution, or the time with the highest probability of occurrence. This condition is not possible with the normal distribution, which is symmetrical, because the normal distribution requires the mode to be equidistant from the end points of the distribution.Figure 7.6 shows the difference between the two distributions.