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Critical tasks are those tasks that are on the critical path. Critical path is a defined sequence of tasks in the precedent network that must be completed to complete the project on time. It is the longest path in the network. If an activity on the critical path slips, the project complete date will also slip. Critical path is a deterministic calculation that requires both a forward and backward pass through the schedule.
Crucial tasks are calculated using Monte Carlo simulation. A Monte Carlo simulation runs multiple deterministic models of the schedule (iterations). However, in each iteration, the start and finish time, duration, and lag for each activity can vary based on the risks and statistical distributions assigned to each task. Therefore, in one iteration, an activity may have a relatively long duration, in another it may have a relatively low duration. During each iteration, the software monitors how changes in the duration, start, or finish time of the task impacts the project schedule. A correlation between the task variance and project variance is calculated and this becomes the basis of the task’s cruciality. The higher the correlation, the more “crucial” the task becomes to the overall success of the project.
If you compare the crucial and critical activities, normally there will be a significant overlap. However, cruciality identifies those activities that are on or near the critical path that may not be apparent with a critical path analysis.
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