PERT Analysis within CPM

PERT Analysis within CPM: A Comprehensive Guide

Introduction to PERT Analysis within CPM

PERT (Program Evaluation and Review Technique) Analysis is a crucial component of the Critical Path Method (CPM) in project management. This guide will explain what PERT analysis is, why it's important, how it works, and how to approach exam questions on this topic.

Why PERT Analysis is Important

PERT Analysis is essential because it:

1. Addresses uncertainty in project activities
2. Provides statistical probability for project completion dates
3. Helps manage risks in projects with unknown variables
4. Complements CPM by adding probabilistic time estimates
5. Enables project managers to make data-driven decisions about scheduling

What is PERT Analysis?

PERT Analysis is a statistical tool used within the Critical Path Method framework that considers the uncertainty in activity durations. While traditional CPM uses single-point time estimates, PERT incorporates three time estimates for each activity:

- Optimistic time (O): The minimum possible time required if everything proceeds better than expected
- Most likely time (M): The realistic duration under normal conditions
- Pessimistic time (P): The maximum time required if significant problems occur

From these three estimates, PERT calculates the Expected time (TE) using the formula:

TE = (O + 4M + P) ÷ 6

How PERT Analysis Works with CPM

1. Identify all activities in the project
2. Establish dependencies between activities
3. Collect three time estimates (O, M, P) for each activity
4. Calculate the Expected time (TE) for each activity
5. Calculate variance for each activity using: Variance = [(P - O) ÷ 6]²
6. Draw the network diagram using TE values
7. Identify the critical path based on these expected times
8. Calculate project variance by summing the variances of activities on the critical path
9. Determine standard deviation (square root of the total variance)
10. Calculate probability of meeting specific deadlines using normal distribution

Key PERT Formulas to Remember

- Expected time: TE = (O + 4M + P) ÷ 6
- Variance of an activity: V = [(P - O) ÷ 6]²
- Standard deviation: σ = √V
- Z-value for probability: Z = (Target date - Expected completion date) ÷ σ

Exam Tips: Answering Questions on PERT Analysis within CPM

1. Read carefully: Pay attention to whether the question asks for expected time, variance, standard deviation, or probability.

2. Show your work: Include all calculations, especially for expected time and variance.

3. Draw the network diagram: If asked to find the critical path, draw the complete network with forward and backward passes.

4. Remember the formulas: Memorize the PERT formulas as they're fundamental to solving these problems.

5. Watch units: Ensure time units are consistent (days, weeks, hours) throughout your calculations.

6. Probability questions: For questions asking about the probability of completing by a certain date:
- Calculate Z-value using the formula above
- Use a standard normal distribution table or the empirical rule
- For Z-values: Z=1 (84% probability), Z=2 (97.5% probability), Z=3 (99.7% probability)

7. Critical path focus: Remember that variance is only summed for activities on the critical path.

8. Verify critical path: The critical path may change when using expected times instead of single-point estimates.

9. Interpret results: Be prepared to explain what the probability values mean in the context of project management.

10. Practice with scenarios: Work through practice problems that combine CPM and PERT to gain confidence.

Common Exam Question Types

1. Calculating expected time from three estimates
2. Finding variance and standard deviation
3. Determining the probability of completing a project by a specific date
4. Comparing PERT estimates with single-point CPM estimates
5. Identifying the critical path using PERT times
6. Analyzing the impact of reducing variance on project outcomes

By mastering PERT Analysis within CPM, you'll have a powerful tool for managing projects with uncertain activity durations and be well-prepared for exam questions on this important topic.