PERT cheat sheet

AON (precedence diagramming) places activities on nodes and dependencies on arrows; AOA places activities on arrows and needs dummy activities to preserve correct logic.

Four dependency types exist: finish-to-start (FS, the most common), start-to-start (SS), finish-to-finish (FF), and start-to-finish (SF).

Lag is a positive wait added to a dependency; lead is a negative lag that creates overlap between predecessor and successor.

A dummy activity has zero duration and consumes no resources; in AOA it carries logic and prevents two activities from sharing the same start and finish nodes.

A valid network is acyclic - a loop implies an activity precedes itself, so early-start/early-finish calculations cannot terminate.

Mandatory (hard-logic, contractual) dependencies differ from discretionary (soft-logic, team-chosen) dependencies; external dependencies tie project work to non-project activities.

A merge activity has multiple predecessors; a burst activity has multiple successors; both affect how float is distributed through the network.

Every activity except the start milestone requires at least one predecessor, and every activity except the finish milestone requires at least one successor.

The number of distinct paths grows combinatorially with network size, so path enumeration or CPM computation replaces visual inspection.

Expected duration: TE = (O + 4M + P) / 6.

Standard deviation: sigma = (P - O) / 6; variance = sigma^2 = ((P - O) / 6)^2.

Weights: M carries 4/6 while O and P carry 1/6 each, pulling TE toward the most likely value.

Triangular alternative: mean = (O + M + P) / 3, used when the beta assumption is not justified; it gives less weight to M.

Classic PERT assumes a beta distribution bounded by O and P, permitting skew; activity durations are not assumed normal.

Confidence bands for a normal curve: plus/minus 1 sigma is about 68.3%, 2 sigma about 95.4%, 3 sigma about 99.7%.

If (P - M) exceeds (M - O) the estimate is right-skewed and TE is greater than M; the reverse gives left skew and TE below M.

A wider (P - O) span produces a larger sigma and higher activity risk even when TE is unchanged.

Range estimates should come from the person doing the work; three-point outputs feed both the CPM network and schedule simulation.

Forward pass: ES = maximum EF of predecessors; EF = ES + duration.

Backward pass: LF = minimum LS of successors; LS = LF - duration.

Total float: TF = LS - ES = LF - EF; float is shared along a chain rather than owned by a single activity.

Free float: FF = minimum ES of successors minus the activity's EF; it is the slip that disturbs no immediate successor's early start.

The critical path is the longest path through the network and equals the shortest feasible project duration; its activities normally carry zero total float.

When several paths tie for longest, all are critical, so any slip on any of them delays the project finish date.

Negative total float means the imposed deadline is earlier than the calculated early finish; the plan must be compressed or the date renegotiated.

A near-critical path carries small positive float and becomes critical once upstream work slips.

Zero float establishes criticality; resource leveling can later shift dates but does not change which logic path is longest.

Path variance equals the sum of activity variances on that path; path sigma = square root of the summed variance. Standard deviations are never summed.

Z = (Target date - TE of path) / sigma of path; convert Z to a probability using a standard normal table.

The probability of finishing by TE is 50% because the normal curve is symmetric; later dates give probabilities above 50%, earlier dates below 50%.

P80 requires Z of about 0.84, P90 about 1.28, and P95 about 1.65, each applied as multiples of path sigma above TE.

Merge bias: converging parallel paths raise the chance that at least one predecessor is late, so single-path PERT understates total schedule risk.

Positive correlation among activity durations increases path variance relative to the independence assumption.

The critical path usually drives the probability calculation, but simulation can reveal a near-critical path as the true risk driver.

Monte Carlo simulation samples each activity distribution repeatedly and reports the full completion distribution (P50, P80, P90).

The required confidence level sets the contingency reserve: a reserve sized to P80 leaves roughly a 20% chance of overrun.