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PERT/Activity Diagrams, Completion Probability and the Z Score

PERT/Activity Diagrams, Completion Probability and the Z Score. Source: Bob Hugg , Thinking in Project Management Terms. Activity diagraming (CPM). Define the goal of the project and the tasks required to complete it Place tasks in a logical order and determine the critical path

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PERT/Activity Diagrams, Completion Probability and the Z Score

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  1. PERT/Activity Diagrams,Completion Probability and the Z Score Source: Bob Hugg, Thinking in Project Management Terms EECS811: IT/Software Project Management

  2. Activity diagraming (CPM) • Define the goal of the project and the tasks required to complete it • Place tasks in a logical order and determine the critical path • The critical path is the longest time path through the network of tasks EECS811: IT/Software Project Management

  3. PERT • So far, we considered models with “single time estimates” for activity durations (e.g., with the CPM) • PERT requires three estimates for each activity • Generate a set of duration estimates for each task • An optimistic, a most likely, and a pessimistic • Label as a, b, m, or as TO, TL, TP • Most likely time (m): Activity duration under normal circumstances • Optimistic time (a): Shortest time to complete the activity • Pessimistic time (b): Worst possible time to complete the activity EECS811: IT/Software Project Management

  4. Calculate PERT for each task • TE = (TP + 4TL + TO)/6 • Complete the above for all tasks • The sum of duration of tasks on the critical path will determine the project duration EECS811: IT/Software Project Management

  5. Calculate standard deviation and variance • Standard deviation is the average deviation from the estimated time • As a general rule: the higher the SD, the greater the amount of uncertainty) • SD = (TP – TO)/6 • Variance reflects the speared of a value over a normal distribution • V = (SD)2 • SD and V are very useful in determining the probability of a project meeting its desired completion time EECS811: IT/Software Project Management

  6. What is standard deviation? • The standard deviation provides some idea about the distribution of scores around the mean (average) • The smaller the standard deviation, the more narrow the range between the lowest and highest scores • The scores cluster closely to the average score EECS811: IT/Software Project Management

  7. Sample table for the estimates EECS811: IT/Software Project Management

  8. Consider the following tasks and activity diagram EECS811: IT/Software Project Management

  9. Populate table with sample data EECS811: IT/Software Project Management

  10. Table of estimates with start dates EECS811: IT/Software Project Management

  11. Determine completion probability • A wealth of information in the above table • Critical tasks, non-critical tasks, best and worst estimates and the expected duration for each, SD and V values • Calculate probability of project completion on a desired date • S: the sum of all expected durations on the critical path • V: the sum of all variances on the critical path • D: Select a desired completion time • Compute Z = (D-S)/ • Look up the value of Z (e.g., here) EECS811: IT/Software Project Management

  12. An example • What is the probability of completing the project in 15 days? • Z = (D-S) / = (15 – 15.51) / = -0.51/1.59 Z = -.321 • A corresponding probability value for Z is 37.7% • There is 38% probability that the project will be completed within 15 days of the start day EECS811: IT/Software Project Management

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