PERT Formula (Program Evaluation and Review Technique)

 

Summary of the PERT Formula (Program Evaluation and Review Technique)

1. Definition:

   • The PERT formula is a statistical tool used in project management to estimate the duration or cost of an activity based on three values:
     1. Optimistic (O): Best-case scenario.
     2. Realistic (R): Most likely scenario.
     3. Pessimistic (P): Worst-case scenario.

2. Purpose:

   • To calculate a weighted average duration or cost for an activity.
   • To account for uncertainties and variability in estimates, providing a realistic forecast.

3. PERT Formula:

   • Expected Duration (E): $$E = \frac{O + 4R + P}{6}$$
     • This formula gives more weight to the realistic estimate (4R).

4. Standard Deviation:

   • Measures the range of uncertainty in the estimate: $$\text{Standard Deviation (SD)} = \frac{P - O}{6}$$
     • Indicates the expected variation from the mean estimate.

5. Triangular Distribution:

   • A simpler average of the three values: $$E = \frac{O + R + P}{3}$$
     • Does not weight the realistic estimate and is less commonly used.

6. Example:

   • Scenario: Estimate the time to paint a room.
     • Optimistic (O): 2 days.
     • Realistic (R): 4 days.
     • Pessimistic (P): 12 days.
   • Calculate Expected Duration (PERT): $$E = \frac{2 + 4(4) + 12}{6} = \frac{2 + 16 + 12}{6} = \frac{30}{6} = 5 \text{ days.}$$
   • Calculate Standard Deviation (SD): $$SD = \frac{P - O}{6} = \frac{12 - 2}{6} = \frac{10}{6} = 1.7 \text{ days.}$$
   • Range of Estimate:
     • $5 \pm 1.7$: The activity will take between 3.3 and 6.7 days.

7. Second Example:

   • Scenario: Estimate time for another task.
     • Optimistic: 10 days.
     • Realistic: 15 days.
     • Pessimistic: 40 days.
   • Calculate Expected Duration: $$E = \frac{10 + 4(15) + 40}{6} = \frac{10 + 60 + 40}{6} = \frac{110}{6} \approx 18.3 \text{ days.}$$
   • Standard Deviation: $$SD = \frac{P - O}{6} = \frac{40 - 10}{6} = \frac{30}{6} = 5 \text{ days.}$$

8. Applications:

   • Exams (PMP, CAPM):
     • PERT is a commonly tested concept; know the formulas and practice calculations.
   • Real Life:
     • Used in government projects and large-scale organizations to estimate timelines and budgets.
     • Tools like Microsoft Project support PERT calculations.

9. Advantages:

   • Provides a more realistic estimate by weighting the most likely outcome.
   • Incorporates uncertainty and helps account for risks in activity durations.

10. Highlighted Points:

    • Memorize the PERT formula: $$E = \frac{O + 4R + P}{6}$$
    • Understand the difference between PERT (weighted average) and Triangular Distribution (simple average).
    • Use the Standard Deviation formula to calculate the range of estimates.

Key Takeaway:

The PERT formula is a valuable tool for estimating durations or costs with realistic and data-driven precision. It considers uncertainty, improves planning accuracy, and is widely used in exams and real-life projects. "Estimate thoroughly, account for risks, deliver confidently."