Network diagram vs. PERT chart

A network diagram is a picture of logic

PMI’s Lexicon of Project Management Terms defines a project schedule network diagram as:

“A graphical representation of the logical relationships among the project schedule activities.”

It answers one question: what must happen before what? Durations, dates, and float are layered onto it afterward by the critical path method. It carries no probability of any kind.

PERT is a way of estimating

The same lexicon defines PERT as:

“A technique used to estimate project duration through a weighted average of optimistic, pessimistic, and most likely activity durations when there is uncertainty with the individual activity estimates.”

It answers a different question: how confident are we in the duration? It needs a network to run on, but the network is not the technique.

Why the terms collapsed into each other

The historical PERT chart was drawn in the activity-on-arrow (event-oriented) style. Wikipedia records that PERT relies:

“on arrow and node diagrams of activities and events: arrows represent the activities or work necessary to reach the events or nodes that indicate each completed phase of the total project.”

Because that arrow-style drawing was for decades the only network most managers ever saw, “PERT chart” became a loose label for any schedule network. Today, per the Wikipedia article on the critical path method:

“Although the activity-on-arrow diagram (PERT chart) is still used in a few places, it has generally been superseded by the activity-on-node diagram, where each activity is shown as a box or node and the arrows represent the logical relationships going from predecessor to successor.”

The same workflow, drawn both ways

One two-step workflow — write a draft, then edit it. The work does not move; the drawing convention moves it. Watch which element holds the duration.

Where Microsoft Project actually sits — in Microsoft’s own words

The view is not called a PERT chart. Microsoft’s support page states:

“A Network Diagram is a graphical way to view tasks, dependencies, and the critical path of your project… Boxes (or nodes) represent tasks, and dependencies show up as lines that connect those boxes.”

Microsoft reserves the word PERT for the estimate, not the drawing:

“You can enter the expected duration as part of a PERT analysis calculation, which takes a weighted average of expected, pessimistic, and optimistic dates and durations… By default, the PERT analysis calculation gives the heaviest weight (4) to the expected information, and the lightest weight (1 each) to the pessimistic and optimistic information.”

That is the same three-point technique the PMI lexicon defines — carried out in a table of task fields, with no arrows involved.

A number written on an activity-on-node link is therefore never the predecessor’s duration. It is lead or lag:

“When you add lead time to a task, work on that task overlaps work on its predecessor. When you add lag time, you delay the start time of the successor task… Lag time creates a delay between two tasks that share a dependency.”

Writing “FS − 5 d” next to a 5-day predecessor mixes the two: as an annotation it would mean a five-day lead, pulling the successor five days earlier.

Not supported by any source cited here: that Microsoft invented or flipped the convention, or that it did so because data is hard to print on a line. None of the Microsoft pages above gives a reason.

Quotations below reproduce the source wording exactly. Bracketed numbers link to the source. Where a term has no definition in PMI’s lexicon, the alternative source is named on the row.

From the PMI Lexicon of Project Management Terms [1]

Project schedule network diagram

“A graphical representation of the logical relationships among the project schedule activities. See also node and precedence diagramming method (PDM).”

Precedence diagramming method (PDM)

“A technique used for constructing a schedule model in which activities are represented by nodes and are graphically linked by one or more logical relationships to show the sequence in which the activities are to be performed.”

Activity

“A distinct, scheduled portion of work performed during the course of a project.”

Milestone

“A significant point or event in a project, program, or portfolio.”

Critical path

“The sequence of activities that represents the longest path through a project, which determines the shortest possible duration.”

Critical path method

“A method used to estimate the minimum project duration and determine the amount of scheduling flexibility on the logical network paths within the schedule model.”

Early start date

“In the critical path method, the earliest possible point in time when the uncompleted portions of a schedule activity can start based on the schedule network logic, the data date, and any schedule constraints.”

Early finish date

“In the critical path method, the earliest possible point in time when the uncompleted portions of a schedule activity can finish based on the schedule network logic, the data date, and any schedule constraints.”

Late start date

“In the critical path method, the latest possible point in time when the uncompleted portions of a schedule activity can start based on the schedule network logic, the project completion date, and any schedule constraints.”

Late finish date

“In the critical path method, the latest possible point in time when the uncompleted portions of a schedule activity can finish based on the schedule network logic, the project completion date, and any schedule constraints.”

Forward pass

“A critical path method technique for calculating the early start and early finish dates by working forward through the schedule model from the project start date or a given point in time.”

Backward pass

“A critical path method technique for calculating the late start and late finish dates by working backward through the schedule model from the project end date.”

Total float

“The amount of time that a schedule activity can be delayed or extended from its early start date without delaying the project finish date or violating a schedule constraint.”

Free float

“The amount of time that a schedule activity can be delayed without delaying the early start date of any successor or violating a schedule constraint.”

Three-point estimating

“A technique used to estimate cost or duration by applying an average or weighted average of optimistic, pessimistic, and most likely estimates when there is uncertainty with the individual activity estimates.”

Program evaluation and review technique (PERT)

“A technique used to estimate project duration through a weighted average of optimistic, pessimistic, and most likely activity durations when there is uncertainty with the individual activity estimates.”

PERT-specific vocabulary [3]

PERT event

“A point that marks the start or completion of one or more activities. It consumes no time and uses no resources. When it marks the completion of one or more activities, it is not “reached” (does not occur) until all of the activities leading to that event have been completed.”

Expected time

“The best estimate of the time required to accomplish an activity (te) or a path (TE), accounting for the fact that things don’t always proceed as normal (the implication being that the expected time is the average time the task would require if the task were repeated on a number of occasions over an extended period of time).”

Standard deviation of time

“The variability of the time for accomplishing an activity (σte) or a path (σTE).”

Critical path (PERT wording)

“The longest possible continuous pathway taken from the initial event to the terminal event. It determines the total calendar time required for the project; and, therefore, any time delays along the critical path will delay the reaching of the terminal event by at least the same amount.”

Float / slack (PERT wording)

“Float or slack is a measure of the excess time and resources available to complete a task. It is the amount of time that a project task can be delayed without causing a delay in any subsequent tasks (free float) or the whole project (total float).”

Network diagram types

“There are two types of network diagrams, activity on arrow (AOA) and activity on node (AON).”

Dummy activity (project-management-knowledge.com) [5]

“A dummy activity is a zero-duration placeholder used in the arrow diagramming method (ADM, also called activity-on-arrow) to show a logical dependency between two activities that cannot be represented with an ordinary arrow. It carries no work and no time — it exists only to keep the network diagram’s logic correct.”

Origin, in the sources’ own words

“PERT was originally developed by Charles E. Clark for the United States Navy in 1958; it is commonly used in conjunction with the Critical Path Method (CPM), which was also introduced in 1958. It was developed by the United States Navy Special Projects Office, Lockheed Aircraft, and Booz Allen Hamilton to support the Navy’s Polaris missile project.”

“PERT was introduced as an event-oriented, probabilistic technique to increase the Program Manager’s control in projects where time was the critical factor and time estimates were difficult to make with confidence.”

“The CPM is a project-modeling technique developed in the late 1950s by Morgan R. Walker of DuPont and James E. Kelley Jr. of Remington Rand.”

In the precedence diagramming method the activity lives in the box. The six numeric fields below are the standard CPM node; every scheduling tool exposes the same six, whatever it calls them.

The four logical relationship types

PDM links nodes with dependencies. The arrow’s meaning changes with the relationship type — this is precisely what an activity-on-arrow PERT chart cannot express.

Seven activities from a clinical-trial site-startup sequence. Top row of each box: ES │ DUR │ EF. Bottom row: LS │ TF │ LF. Zero-float boxes and their links are the critical path: A → C → D → F → G = 5 + 7 + 15 + 3 + 2 = 32 days.

Forward pass — verbatim rules

PMI’s CPM primer states the two forward-pass formulas exactly as:

• Early Start = Maximum (or Highest) EF value from immediate Predecessor(s)
• Early Finish = ES + Duration

“The first step in the calculation process is known as the Forward Pass. In the forward pass, the Early Start and Early Finish values for each activity, along with the overall Project Duration, are calculated.”

F has three predecessors — B (EF 15), D (EF 27), E (EF 13). ES_F = max(15, 27, 13) = 27. The merge takes the latest, never the average.

Backward pass — verbatim rules

• Late Start = LF − Duration
• Late Finish = Minimum (or Lowest) LS value from immediate Successor(s)
• Total Float = LS − ES (it is also calculated by LF − EF)
• Free Float = Lowest ES of successors − EF

“The second step in the calculation is comprised of the Backward Pass. Through this pass, the Late Start and Late Finish values are calculated.”

A has three successors — B (LS 17), C (LS 5), E (LS 19). LF_A = min(17, 5, 19) = 5, so LS_A = 5 − 5 = 0 and TF_A = 0. A is critical because of C alone.

Project duration = 32 working days. Every path: A-B-F-G = 20; A-E-F-G = 18; A-C-D-F-G = 32. The longest is the critical path, matching the lexicon wording “the longest path through a project, which determines the shortest possible duration.” [1]

Same seven activities, drawn the original PERT way. Here the arrow is the work and the circle is an event — “a point that marks the start or completion of one or more activities” that “consumes no time and uses no resources” [3]. Note what appears that AON never needs: a dummy.

The parts of a PERT chart, one by one

Circle / node

An event or milestone — a state, not work. Numbered so activities can be named by their start-end pair (activity 2-5 is B).

Arrow

An activity — the work and the time. Length carries no meaning; the label carries the duration.

Dashed arrow

A dummy activity — logic only, zero duration, zero resources.

Initial event

Event 1. No predecessors; the origin of the forward pass.

Terminal event

The last event. The longest possible continuous pathway taken from the initial event to the terminal event defines the critical path [3].

Merge event

Event 5 here. Not reached until all of the activities leading to that event have been completed [3].

Burst event

Event 2 here — one event, several activities starting from it.

te on the arrow

Expected time, not a raw duration. This is the part that makes the chart PERT rather than just a network.

The PERT arithmetic

Wikipedia states the two formulas as te = (o + 4m + p) / 6 and TE = Σ te, with σte = (p − o) / 6 and σTE = √(Σ σte²) [3]. The defense reference states the same expected time as (P+4M+O)/6 and notes “an expected time is calculated based on a beta probability distribution for each activity from these estimates.” [6]

Worked: for D, te = (10 + 4·14 + 30) / 6 = 96/6 = 16.00; σ = (30 − 10)/6 = 3.33; σ² = 11.11. D alone contributes 78% of the whole path’s variance — the single most useful thing PERT tells you about this schedule, and something the deterministic 32-day network cannot say at all.

Probability of finishing on or before a target date

z = (target − TE) / σTE, with TE = 34.33 and σTE = 3.79:

• 32.0 d (the CPM answer) → 27%
• 34.3 d (TE) → 50%
• 40.0 d → 93%

They are not alternatives — they compose

Nothing stops you from putting PERT expected times into an activity-on-node network: run three-point estimating per activity, use te as the duration, run the forward and backward passes, then attach σTE to the answer. That is the normal modern practice, and it is why the terms drifted together. The precise sentence is: a PERT chart is one historical style of network diagram; PERT estimating is a technique that any network diagram can carry.

Four claims to stop repeating

• “A PERT chart shows time to scale.” It does not. Arrow length is arbitrary in both forms; a Gantt bar chart is the time-scaled view.
• “PERT finds the critical path, CPM does not.” Both do. They differ in whether the duration is one number or three.
• “Microsoft Project’s Network Diagram is a PERT chart.” Microsoft calls it the Network Diagram, describes it as boxes for tasks and lines for dependencies [8], and applies the word PERT only to the weighted three-point PERT analysis calculation on task fields [9].
• “The PERT date is safe.” TE is a mean — roughly a coin flip. A commitment date needs a stated confidence level, as in the panel above.

All quotations above are verbatim from these documents. PMI’s lexicon is the authority for the schedule-model vocabulary; the remaining sources supply the formulas and the PERT-specific terms the lexicon does not define.

1. PMI Lexicon of Project Management Terms (Project Management Institute) — verbatim definitions of project schedule network diagram, precedence diagramming method, activity, milestone, critical path, critical path method, early/late start and finish, forward and backward pass, total and free float, three-point estimating, and PERT.
2. Understanding the basics of CPM calculations — Project Management Institute — verbatim forward-pass, backward-pass, total float and free float formulas.
3. Program evaluation and review technique — Wikipedia — PERT event, expected time, standard deviation of time, float/slack, the two network diagram types, and the 1958 Navy/Polaris origin.
4. Critical path method — Wikipedia — the supersession of the activity-on-arrow (PERT chart) form by activity-on-node, and CPM’s DuPont / Remington Rand origin.
5. Dummy Activity in the Arrow Diagramming Method Explained — Project Management Knowledge — verbatim definition of the dummy activity and of the activity-on-node form’s four logical relationship types.
6. Program Evaluation and Review Technique (PERT) Analysis — AcqNotes — PERT as an event-oriented, probabilistic technique, the expected-time formula (P+4M+O)/6, and the beta-distribution basis.
7. Project Schedule Network Diagram — Project-Management.info and PDM — Precedence Diagramming Method — the AON / AOA presentation distinction and PDM as a technique of the “sequence activities” process.
8. Create a Network Diagram in Project desktop — Microsoft Support — the name of the view, and “Boxes (or nodes) represent tasks, and dependencies show up as lines that connect those boxes.”

Sources 9–10 (Microsoft PERT analysis and lead/lag documentation) are Microsoft Support pages quoted in §01.