# Unit 6-3 Project Evaluation & Review Technique

The Project Evaluation and Review Technique (PERT) is used more often in project environments where there is more uncertainty. Instead of deterministic times for tasks, we assume the task times follow some probability distribution.  One such distribution is the beta distribution and each task starts with three estimates of task duration, an optimistic time a, most likely time m and a pessimistic time b. Using the beta distribution, the estimated time is Te= (a+4m+b)/6

From the time estimates we can also determine the variance associated with the task duration.  Assuming that the time durations are estimated with 99% probability then the variance of each task duration is calculated as follows σ2= (ba/6)2

The approach for determining the project schedule and completion time is the same as for the CPM method. However, this approach also allows us to estimate probability of project completion for a given duration or to estimate completion time associated with a given probability . Let’s use an example to illustrate.

Given a project with the following task durations we want to find the completion time and the probability of finishing the project in :

 Activity Predecessor a m b Expected Time Variance A – 6 7 14 B – 8 10 12 C A 2 3 4 D A 6 7 8 E B,C 5 5.5 9 F B,C 5 7 9 G D,E 4 6 8 H F 2.5 3 3.5

Here are the steps involved:

I.       Determine the expected time and variance for each task

II.         Identify the critical path

II.         Determine expected completion time

III. Calculate total variance for activities on critical path;

IV. Calculate the standard deviation

IV.       Calculate the Z value

V.        Determine probability from normal distribution table

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