6.2 Monte Carlo Simulation, Criticality, Correlation, and Merge Effects

6.2 Monte Carlo Simulation, Criticality, Correlation, and Merge Effects

A deterministic CPM calculation uses one value for each duration and one defined network. Monte Carlo schedule analysis instead samples uncertain inputs many times, recalculates the schedule for each iteration, and records the resulting milestone dates and path behavior. The collection of results forms a distribution conditioned on the model and inputs.

AACE RP 57R-09 addresses integrated cost and schedule risk analysis using risk drivers and Monte Carlo simulation of a CPM schedule. RP 65R-11 concerns integrated expected-value methods; it should not be cited as the Monte Carlo CPM practice.

Simulation workflow

For each iteration, the model generally:

1. samples duration uncertainty and any modeled risk-event occurrence and impact;
2. applies correlation or shared risk-driver behavior as defined;
3. recalculates schedule dates through the network;
4. records selected milestones, path membership, float, and risk results; and
5. repeats until the analyst has enough stable output for the decision.

Before simulation, verify scope, logic, calendars, status, constraints, and the data date. A missing interface remains missing in every iteration. An unjustified constraint can suppress the path changes the analysis is intended to reveal.

Sampling and convergence

Simple random sampling draws independent probability values from each input distribution. Latin Hypercube Sampling (LHS) divides each input’s cumulative probability range into equal-probability strata and samples each stratum once, then pairs samples across inputs. This stratification can provide better input coverage than simple random sampling at the same sample size.

LHS does not guarantee an exact tail percentile, preserve every desired correlation automatically, or establish that a fixed number of iterations is sufficient. Check convergence of the decision-relevant outputs by comparing results as the sample grows or by using repeated runs. Tail estimates often require more attention than central estimates because fewer simulated observations describe extreme portions of the output.

Criticality and sensitivity

A criticality index commonly reports the percentage of iterations in which an activity satisfies the model’s critical-path criterion. The exact criterion can depend on the tool and settings—for example, zero or near-zero float, longest-path membership, or another threshold. State the definition used.

An activity can be noncritical in the deterministic model yet have a high criticality index because sampled durations cause its path to become controlling in many iterations. A high index identifies frequent path participation; it does not by itself show that reducing the activity will yield the greatest milestone benefit.

Sensitivity or correlation measures describe how variation in an input or activity duration is associated with variation in a milestone outcome. Criticality and sensitivity can diverge. A frequently critical activity with little uncertainty may contribute less variation than an uncertain activity that becomes critical less often. Review both the measure and its limits before prioritizing mitigation.

Merge effects

When several paths converge at a milestone, the milestone cannot occur until all required predecessors are complete. If three independent paths each have a 60% probability of finishing by Day 90, the probability that all three finish by Day 90 is:

$0.60 \times 0.60 \times 0.60 = 0.216 = 21.6\%$

The multiplication is valid only under the stated independence assumption. If paths share weather, labor, design information, or other drivers, their outcomes may be correlated and the simple product may be wrong. Simulation is useful because it can represent varied path distributions and explicit dependence.

The expected maximum of converging uncertain paths is often later than a schedule built from single central durations, but do not turn that tendency into a universal claim that every deterministic schedule is late. The size and direction of the difference depend on the chosen deterministic values, distributions, dependence, logic, and constraints.

Correlation and risk drivers

Activities may move together because they share a cause. Weather can affect several outdoor scopes, a design-system issue can affect multiple releases, and a supplier event can affect fabrication and delivery. Dependence may be represented with correlations, risk drivers mapped to multiple activities, or explicit scenarios. Each method requires a documented basis.

Ignoring material positive dependence can make a distribution unrealistically narrow. Adding arbitrary correlation can also distort the result. Check that the correlation structure is feasible and does not double-count an effect already included in duration ranges or discrete risks.

Review questions

Before relying on the output, ask:

• Are input ranges tied to quantities, productivity, records, or facilitated expert judgment?
• Are discrete events separated from ordinary duration uncertainty?
• Are shared drivers and correlations traceable?
• Do deterministic and sampled networks preserve valid logic and calendars?
• Are milestone percentiles stable enough for the decision?
• Have sensitivity tests challenged important assumptions?

Monte Carlo output supports a decision; it is not a guarantee. Communicate the model date, confidence date, assumptions, exclusions, influential drivers, and actions that could change the distribution.