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)/ v
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) / v = (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