Interactive Project Management Demonstration

PERT Analysis

Use three-point estimates to calculate expected activity durations and uncertainty, build the expected schedule, identify the critical path, combine critical-path variance, and estimate the probability of meeting a target completion date.

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Demonstration at a glance
Level Intermediate
Typical duration 10–15 minutes
Learning format Guided uncertainty simulation
Best for Project managers, planners and certification learners
Demonstration overview

Turn Three-Point Estimates into a Probabilistic Schedule.

PERT analysis represents activity duration uncertainty with optimistic, most likely, and pessimistic estimates. The demonstration converts those estimates into expected activity durations and variances, then combines schedule logic with uncertainty to estimate the probability of meeting a target project completion date.

  • Review optimistic (O), most likely (M), and pessimistic (P) estimates.
  • Calculate the PERT expected duration for each activity.
  • Calculate activity standard deviation and variance.
  • Build the expected-duration Activity-on-Node network.
  • Calculate the expected schedule and identify the critical path.
  • Combine critical-path variance to determine project standard deviation.
  • Calculate a Z-score and approximate completion probability for a target date.
Guided Demonstration

PERT Analysis — Step by Step

Complete each stage before the next stage unlocks. Every reveal changes the PERT visual so the calculation and its schedule consequence remain visible together.

Learning stages
Foundation Stage 1 of 8

Review the Three-Point Estimate Data

Current instruction
Interactive PERT Visual

Three-Point Estimates, Network and Uncertainty

Three-point estimates are revealed activity by activity.

100%
Three-point estimates Expected time / schedule Variance / uncertainty Critical path

Focus Mode moves you to the Guided Demonstration, then hides the rest of the page while keeping the current learning stage and PERT visual together. Zoom affects only the visual pane.

PERT status: Review the three-point estimates, then calculate expected durations.
Supporting Calculation Table

PERT Schedule Values

The table mirrors the guided sequence. Values appear only after the corresponding calculation has been completed.

Activity Predecessor(s) O M P Expected Time Std. Dev. Variance ES EF Total Float
Experiment Mode

Change an Activity Estimate and the Target Date

Experiment Mode is isolated from the guided example. Select an activity, change its three-point estimates, and test a target completion date to see how the expected project duration, critical path, project uncertainty, and completion probability respond.

Expected duration 12.33
Critical path A → D → E → F
Project σ 0.88
Completion probability 77.5%
Check Your Understanding

Quick Knowledge Check

Choose an answer, then check it.
PERT Quick Reference

Core Formulas and Interpretation

Calculation Formula / Rule Interpretation
Expected Time TE = (O + 4M + P) / 6 Weighted expected activity duration.
Activity Standard Deviation σ = (P − O) / 6 Spread of the activity-duration estimate.
Activity Variance Variance = [(P − O) / 6]² Squared uncertainty used for aggregation.
Project Variance Sum activity variances on the selected critical path Approximate critical-path schedule uncertainty.
Project Standard Deviation σproject = √(Project Variance) Spread around the expected project duration.
Z-score Z = (Target − Expected Duration) / σproject Number of project standard deviations between the target and expected duration.
Completion Probability Φ(Z) Approximate probability of finishing by the target date.
Important modelling note: the classical PERT completion-probability calculation is an approximation. It typically sums variances on the selected critical path, assumes activity-duration independence for that calculation, and uses a normal approximation for project completion. It does not fully model critical-path switching or correlated activity durations.
Expected Time → (O + 4M + P) / 6
Variance → [(P − O) / 6]²
Target Probability → Φ(Z)