Program Evaluation and Review Technique (PERT)

Program Evaluation and Review Technique (PERT) Analysis: A Comprehensive Guide

Why PERT Analysis is Important in Risk Management

Program Evaluation and Review Technique (PERT) analysis is a critical tool in project risk management for several reasons:

- It provides a systematic approach to estimate project durations when facing uncertainty
- It helps project managers account for variability in task completion times
- It offers more realistic schedule estimates than single-point estimations
- It supports better decision-making by considering best-case, most likely, and worst-case scenarios
- It's particularly valuable for complex projects with interdependent activities
- It's recognized by PMI as an essential quantitative risk analysis technique

What is PERT Analysis?

PERT analysis is a statistical tool used in project management to analyze and represent the tasks in a project. Developed in the 1950s by the U.S. Navy for the Polaris submarine missile program, PERT specifically focuses on time as the variable factor, helping to determine realistic project schedules when activity durations are uncertain.

Unlike deterministic models that use single-point estimates, PERT uses three time estimates for each activity:

- Optimistic time (O): Best-case scenario - the minimum time required
- Most likely time (M): Most realistic estimate - the expected time
- Pessimistic time (P): Worst-case scenario - the maximum time required

These three estimates are combined to calculate an expected duration using a weighted average formula, giving more weight to the most likely estimate.

How PERT Analysis Works

1. Formula and Calculation
The PERT formula for calculating expected time (E) is:

E = (O + 4M + P) ÷ 6

This weighted average gives four times the weight to the most likely estimate compared to the optimistic and pessimistic estimates.

2. Standard Deviation
PERT also calculates the standard deviation (σ) for each activity:

σ = (P - O) ÷ 6

This measures the uncertainty or variability in the activity duration.

3. Variance
The variance (V) is the square of the standard deviation:

V = [(P - O) ÷ 6]²

4. Probability Calculations
Using standard deviation, project managers can calculate the probability of completing the project within a specific timeframe using normal distribution properties.

Example of PERT Calculation

For an activity with the following estimates:
- Optimistic (O): 4 days
- Most Likely (M): 6 days
- Pessimistic (P): 10 days

Expected duration (E) = (4 + 4×6 + 10) ÷ 6 = 38 ÷ 6 = 6.33 days
Standard deviation (σ) = (10 - 4) ÷ 6 = 1 day
Variance (V) = 1² = 1

Advantages of PERT Analysis

- Accounts for uncertainty in project scheduling
- Provides a range of possible outcomes rather than a single estimate
- Enables probability-based decision making
- Helps identify activities with high variability that may need risk responses
- Creates more realistic project schedules

Exam Tips: Answering Questions on PERT

Terminology and Formulas
- Memorize the PERT formula: E = (O + 4M + P) ÷ 6
- Know how to calculate standard deviation: σ = (P - O) ÷ 6
- Understand that variance equals standard deviation squared

Calculation Practice
- Practice calculating expected durations with various time estimates
- Learn to add variances along the critical path (they are additive)
- Be comfortable using the standard normal distribution table for probability questions

Common Question Types

1. Basic PERT calculations: Given O, M, and P values, calculate the expected duration

2. Standard deviation questions: Calculate the standard deviation for activities or entire projects

3. Probability questions: Determine the likelihood of completing a project by a certain date
Example: "What is the probability of completing the project in 20 days if the expected duration is 22 days with a standard deviation of 2 days?"
4. Comparative questions: Compare PERT with other estimation techniques like CPM (Critical Path Method)

5. Application questions: Decide when PERT is appropriate versus other methods

Key Points to Remember for Exams

- PERT uses weighted averages that emphasize the most likely scenario
- The larger the difference between pessimistic and optimistic times, the greater the uncertainty
- For the entire project, only add variances along the critical path
- The central limit theorem applies: as more activities are added, the distribution becomes more normal
- PERT assumes a beta distribution for individual activities and normal distribution for the overall project
- Z-scores can be used to calculate probabilities (Z = (Target date - Expected date) ÷ Project standard deviation)

Practical Application Tips

- Connect PERT analysis to other risk management processes
- Understand how to use PERT results to inform risk responses
- Know when PERT is most beneficial (projects with significant uncertainty)
- Recognize PERT limitations, such as subjective estimates and the assumption of statistical independence

By thoroughly understanding PERT analysis and practicing with example problems, you'll be well-prepared to answer exam questions on this important quantitative risk analysis technique.