Project Management: AON Diagram, Completion Probability, and Confidence Level

b) The Activity on Node diagram is as follows:

I. Earliest and Latest Start: The earliest start time is the earliest time at which an activity can start without delaying the project. The latest start time is the latest time at which an activity can start without delaying the project.

II. Earliest and Latest Finish: The earliest finish time is the earliest time at which an activity can be completed without delaying the project. The latest finish time is the latest time at which an activity can be completed without delaying the project.

III. Activity Descriptor: A brief description of the activity.

IV. Duration and Float: The duration of the activity is the time it takes to complete. The float is the amount of time an activity can be delayed without delaying the project.

V. Earliest time for Completion and Critical Path: The earliest time for completion is the earliest time at which the entire project can be completed. The critical path is the sequence of activities that determines the shortest time in which the project can be completed.

c) The probability of completing the project in 18 months can be calculated using the critical path and the concept of PERT (Program Evaluation and Review Technique). PERT uses three time estimates for each activity: optimistic time (O), most likely time (M), and pessimistic time (P).

To calculate the probability, we need to calculate the expected time (TE) for each activity using the formula: TE = (O + 4M + P) / 6.

Then, we can calculate the expected project completion time (TP) by summing up the expected times for all activities on the critical path.

Finally, we can use the formula: probability = 1 - F(TP / σ), where F is the cumulative distribution function for the normal distribution and σ is the standard deviation of the project completion time.

d) Based on the critical path, the completion date that we are 70% confident of achieving can be calculated using the concept of PERT.

First, we need to calculate the expected time (TE) for each activity using the formula: TE = (O + 4M + P) / 6.

Then, we can calculate the expected project completion time (TP) by summing up the expected times for all activities on the critical path.

Finally, we can use the formula: completion date = TP + Z * σ, where Z is the Z-score corresponding to the desired confidence level (in this case, 70%) and σ is the standard deviation of the project completion time.