PERT Network Analyzer (Expected Duration & Variance)

PERT Network Analyzer (Expected Duration & Variance) | Online Free Tool | Elysia Tools

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category: Math & Numbers
Input types: textarea, number
Output type: text
Sample coverage: 4
API ready: Yes

Overview

The PERT Network Analyzer performs Program Evaluation and Review Technique calculations using three-point duration estimates (optimistic, most likely, and pessimistic). It computes expected duration and variance for each activity, identifies the critical path across network dependencies, calculates total project expected duration and variance, and determines the probability of meeting an optional target completion deadline.

When to use

Evaluating project schedule risk when task durations involve uncertainty and require three-point estimations.
Identifying the critical path and total expected project duration from a set of dependent activities.
Calculating the statistical probability (Z-score) of completing a project by a specific target deadline.

How it works

1Enter activity details line-by-line with name, optimistic time (a), most likely time (m), pessimistic time (b), and predecessor names.
2The tool calculates the expected duration te = (a + 4m + b) / 6 and variance σ² = ((b - a) / 6)² for each activity.
3The network resolves dependencies to find the critical path, total expected duration (TE), and total critical path variance.
4If an optional target time (T) is provided, the tool calculates Z = (T - TE) / σ and outputs the normal completion probability.

Use cases

Project managers assessing schedule confidence intervals for complex multi-phase initiatives.
Operations research analysts modeling project network dependencies and activity float.
Engineering leads presenting statistical delivery timelines and contingency buffers to stakeholders.

Examples

1. Four-Activity Branching Network

Project Manager

Background

Managing a project with parallel development paths where one branch has high uncertainty.

Problem

Determine which path is critical and evaluate the likelihood of meeting a 16-day schedule deadline.

How to use

Input activities A, B, C, and D with their three-point estimates and predecessor relationships, setting a target completion time of 16.

Activities:
A, 2, 4, 6, -
B, 3, 5, 7, A
C, 2, 3, 10, A
D, 4, 6, 8, B C
Target Time: 16
Decimal Places: 4

Outcome

Identifies the critical path A → B → D with expected duration TE = 15, project variance σ² = 1.3333, and an 80.7% probability of completion by day 16.

2. Serial Chain Milestone Analysis

Operations Analyst

Background

Evaluating a strict sequential process containing three successive execution phases.

Problem

Compute the cumulative expected timeline and variance across the full sequential chain to verify an 18-day target.

How to use

Enter the serial tasks in sequence where each task depends directly on the previous one, and set the target completion time to 18.

FAQ

What format is required for the activity input list?

Enter one activity per line formatted as: name, optimistic (a), most likely (m), pessimistic (b), followed by predecessor names separated by spaces, or '-' if there are no predecessors.

How are expected duration and variance calculated for each activity?

Expected duration uses the standard PERT formula te = (a + 4m + b) / 6, and variance is computed as σ² = ((b - a) / 6)².

How is the total project variance calculated?

Total project variance is calculated by summing the variances (σ²) of only the activities located on the critical path.

What happens if an activity violates the a ≤ m ≤ b rule?

The analyzer validates that the optimistic duration does not exceed the most likely duration, and the most likely does not exceed the pessimistic duration, rejecting invalid entries.

What does the completion probability represent?

Using the standard normal cumulative distribution Φ(Z), it calculates the statistical probability of finishing the project within your specified target time T.

Activities:
A, 1, 3, 5, -
B, 3, 6, 9, A
C, 2, 4, 12, B
Target Time: 18
Decimal Places: 4

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Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Four-Activity Branching Network

2. Serial Chain Milestone Analysis

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