PERTActivity Diagrams Completion Probability and the Z Score

PERT/Activity Diagrams, Completion Probability and the Z Score Source: Bob Hugg, Thinking in Project Management Terms EECS 811: IT/Software Project Management 1

PERT/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 • Generate a set of duration estimates for each task – An optimistic, a most likely, and a pessimistic – Label as a, b, c, or as TO, TL, TP EECS 811: IT/Software Project Management 2

Calculate PERT for each task • TE = (TP + 4 TL + TO)/6 • Complete the above for all tasks • The sum of duration of tasks on the critical path will determine the project duration EECS 811: IT/Software Project Management 3

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 EECS 811: IT/Software Project Management 4

Sample table for the estimates EECS 811: IT/Software Project Management 5

Consider the following tasks and activity diagram EECS 811: IT/Software Project Management 6

Populate table with sample data EECS 811: IT/Software Project Management 7

Table of estimates with start dates EECS 811: IT/Software Project Management 8

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 1. 2. 3. 4. 5. 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) EECS 811: IT/Software Project Management 9

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 EECS 811: IT/Software Project Management 10