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

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

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

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

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

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

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

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

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

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

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

An example What is the probability of completing the project in 15 days? Z = (D-S) / v = (15 – 15.51) / 2.51 = -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