PERT flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Activity-on-Node network

A precedence diagram in which each activity sits on a node and arrows show dependencies; also called precedence diagramming method. No dummy activities are required.

Dummy activity

A zero-duration AOA element drawn as a dashed arrow that carries logic only, preventing two activities from sharing identical start and finish nodes.

Finish-to-Start dependency

The successor cannot begin until the predecessor finishes; this is the most common relationship in project schedules and the default in most scheduling software.

Lead and lag

Lag is a deliberate delay added to a dependency; lead is a negative lag that lets the successor start before the predecessor completes.

Merge and burst activities

A merge activity has two or more predecessors; a burst activity has two or more successors. Both shape network complexity and float distribution.

Network loop prohibition

A valid project network is acyclic; a loop would require an activity to precede itself, making the schedule impossible to compute and logically invalid.

Mandatory versus discretionary dependency

Mandatory dependencies are contractually or legally required, often hard logic; discretionary dependencies are preferred sequencing set by the team and can be changed.

Start-to-Start with lag

A relationship where the successor may start only a specified lag after the predecessor starts; common in overlapping or phased work packages.

PERT expected duration

The formula TE = (O + 4M + P) / 6, in which the most likely estimate is weighted four times and the optimistic and pessimistic estimates once each.

PERT standard deviation

The formula sigma = (P - O) / 6. It measures the spread of an activity duration estimate; a wider optimistic-to-pessimistic span means greater uncertainty.

PERT activity variance

Variance equals ((P - O) / 6) squared, the square of the activity standard deviation. Activity variances are summed to obtain path variance.

Triangular distribution estimate

A simple average, (O + M + P) / 3, used when the beta shape is not justified; it gives the most likely value less weight than PERT does.

Beta distribution assumption

Classic PERT assumes activity durations follow a beta distribution bounded by the optimistic and pessimistic values, allowing skew rather than requiring symmetry around the mean.

Weighting in PERT

The most likely estimate receives four-sixths of the total weight while optimistic and pessimistic each receive one-sixth, pulling the expected value toward M.

Symmetric versus skewed estimates

If the gap from optimistic to most likely exceeds the gap from most likely to pessimistic, the estimate is left-skewed and TE falls below M; the reverse gives right skew.

PERT confidence ranges

Roughly 68.3 percent of outcomes fall within one standard deviation of the mean, 95.4 percent within two, and 99.7 percent within three.

Forward pass

A left-to-right calculation setting early start to the maximum early finish of predecessors and early finish to early start plus duration, yielding earliest possible dates.

Backward pass

A right-to-left calculation setting late finish to the minimum late start of successors and late start to late finish minus duration, yielding latest allowable dates.

Total float formula

TF = LS - ES = LF - EF. It is the amount an activity can be delayed without delaying the project finish, and it is shared along a chain.

Free float

Free float equals the minimum early start of successors minus the activity's early finish. It is the delay possible without affecting any immediate successor.

Critical path

The longest path through the network, which sets the shortest possible project duration; its activities normally carry zero total float.

Multiple critical paths

When two or more paths tie for longest, each is critical, so any delay on any of them slips the project end date.

Negative total float

A negative float value means the imposed finish date precedes the calculated early finish; the schedule must be compressed or the deadline relaxed.

Near-critical path

A path with small but nonzero total float, often within a few days of the critical path; it becomes critical if upstream work slips.

Schedule Z-score

Z equals the target date minus the path expected duration, divided by the path standard deviation. The value is looked up in a normal table.

Path variance

The sum of the variances of the activities on the path, assuming independence. Path standard deviation is the square root of that sum.

Probability at expected duration

Because the normal distribution is symmetric, the probability of finishing by the PERT expected duration is exactly 50 percent.

Merge bias

Understated risk at convergence points: when parallel paths merge, the chance that at least one predecessor is late exceeds any single path's probability.

Monte Carlo simulation

Repeated random sampling of activity duration distributions produces a full project completion distribution, capturing path convergence and correlations that analytic PERT misses.

P80 completion date

The date by which the project has an 80 percent chance of finishing, corresponding to a Z of about 0.84 above the expected duration.

Adding variances, not deviations

Standard deviations cannot be summed across activities; convert each to variance, total them, then take the square root of the total.

Correlation and path variance

Positive correlation among activity durations makes them move together, increasing path variance beyond the value obtained under an independence assumption.