Why cost and schedule risk belong in one model
Many UK projects run a cost QRA and a schedule QRA as separate exercises. The cost team produces an S-curve and a P80 cost. The schedule team produces an S-curve and a P80 completion date. The two are reported side by side. That works on small, short projects with stable scope. On larger ones it leaves out two things: what late finishes cost, and the joint chance of meeting both the budget and the date.
Time drives cost through time-related items: preliminaries, site staff, plant hire, client supervision and finance charges. Suppose these run at £0.5m a week. A 12-week delay then adds 12 x £0.5m = £6.0m before any rework. A cost model that holds the duration fixed cannot see that £6.0m.
Separate QCRA and QSRA are often built from the same register with matched probabilities, and that is sound practice. The remaining gaps are specific. A risk is not forced to occur in both runs of the same iteration, and the simulated duration does not feed time-related cost. An integrated model closes both. Each iteration samples the risks once and returns one completion date and one outturn cost.
The method captures schedule-to-cost effects. It does not model management response running the other way, such as a contractor under cost pressure deferring work. If that behaviour matters, treat it as a scenario or as a risk in its own right.
What EMV gives you and what it misses
Expected monetary value (EMV) is probability multiplied by impact for each risk, summed across the register. AACE International Recommended Practice 44R-08, Risk Analysis and Contingency Determination Using Expected Value, covers the cost method. RP 65R-11, Integrated Cost and Schedule Risk Analysis and Contingency Determination Using Expected Value, is the EMV-based integrated method. EMV is quick and easy to audit, and it suits early stages and short registers.
Take three independent risks: A at 30% x £10m = £3.0m, B at 20% x £8m = £1.6m, C at 50% x £4m = £2.0m. The summed EMV is £6.6m. Enumerating the eight outcomes gives a 28% chance that none occurs (cost £0), a 28% chance that only C occurs (£4m), and a 56% chance of £6.6m or less. The P80 is £12m. A contingency set at EMV leaves a 44% chance of exceeding it, and the P80 is nearly twice the EMV.
EMV returns a mean. It does not give a confidence level, the spread of the total, or the joint outcome of cost and date. It also cannot sum schedule risks. Delay does not add across parallel paths, only critical and near-critical paths move the finish, and the time-related cost of a delay depends on the network. When a client needs a confidence level or the link between date and cost, move to simulation. Keep EMV as a cross-check: the simulated mean cost should be explainable from the summed EMVs plus estimate uncertainty, and a large unexplained gap points to a modelling error.
Two published methods, neither the only one
AACE RP 57R-09, Integrated Cost and Schedule Risk Analysis Using Risk Drivers and Monte Carlo Simulation of a CPM Model, describes one method. It is closely associated with David Hulett's work. RP 65R-11 describes the EMV-based alternative. Neither is the standard approach. Choose by project stage, the quality of the schedule and the question the client needs answered.
A simulation model has four parts: a CPM schedule with cost-loaded activities, summarised to a level suited to risk modelling; a risk register mapped to the activities each risk affects, with probability and cost and schedule impacts; uncertainty ranges on durations and costs, usually three-point estimates; and a simulation engine. In each iteration the engine samples risks and ranges, runs CPM to get a completion date, and calculates cost including time-related items from that duration.
Run enough iterations for the results to settle. Rerun with a different random seed. If P80 cost, P80 date or the joint confidence moves by more than the precision you report, add iterations. State the final count in the report.
Tools in use include Safran Risk, Oracle Primavera Risk Analysis, riskHive Enterprise Risk Manager, Acumen Risk and @RISK (Lumivero). Check each against the same question: does time-related cost respond natively to the simulated duration, or must you build that link by hand? The right tool is usually the one the client's team can support.
Risk drivers and risk events
In the risk-driver method, a driver is a shared cause. It has a probability of occurring and, if it occurs, a multiplicative effect on the duration or cost of every activity mapped to it. Permit approval is an example: one driver, one draw per iteration, applied to every activity that waits on the permit. A risk event is a discrete occurrence recorded in the register with its own impact, usually on a smaller set of activities.
Event registers can also preserve common-cause behaviour. One event mapped to several activities, or events with defined correlation, will move those activities together. The difference lies in how the dependency is represented, maintained and made visible. Drivers hold it in one place that a reviewer can read. Correlation coefficients between many events are harder to audit and easier to set by feel.
A driver model usually has fewer entries than an event register. That makes it easier to challenge. It only helps when the analyst understands the cause. Renaming 'regulatory delay' as 'regulatory approval duration' without re-deciding which activities it affects changes the label and leaves the model as it was.
Worked example: what the joint result looks like
Take a project with a baseline cost of £100m excluding contingency, a baseline duration of 104 weeks and time-related costs of £0.5m a week. The figures are constructed for illustration. Suppose the simulation gives a marginal P80 cost of £118m and a marginal P80 completion of week 120.
The table defines the joint view precisely. For each date percentile, take the iterations whose completion falls within five percentile points either side of that date, and read the 80th percentile of cost within that group. It answers: if the finish lands about here, what cost am I 80% sure of staying under?
Moving from the P50 date to the P80 date adds £10m (£121m less £111m). Eight weeks of extra duration at £0.5m is £4.0m of prolongation. The other £6m is the cost of the risks that caused the late finish, which occurs in the same iterations. A separate cost model reports £118m for every date and shows none of this.
Contingency under each posture, against the £100m baseline. Managing to a cost ceiling: P80 cost of £118m gives £18m. Managing to the week 120 date: £121m gives £21m. Managing to both is covered next.
Two P80s are not an 80% chance of both
If cost has an 80% chance of coming in at or under £118m and the schedule has an 80% chance of finishing by week 120, the chance of achieving both is lower than 80%. Under independence it is 0.8 x 0.8 = 64%. In general it lies between 60% and 80%, whatever the dependency. The floor of 60% (0.8 + 0.8 - 1) applies only under perfect negative dependency.
Cost and schedule are normally positively dependent, because late finishes carry prolongation and the same risks hit both. Positive dependency raises the joint figure above 64%, towards 80% as the dependency strengthens. The actual figure is a model output. In the example the simulation shows 72% of iterations at or under £118m and by week 120. Do not quote a typical value without a model behind it.
If the board wants 80% confidence on both together, set each marginal above P80. The model's joint output gives the pair of percentiles and the contingency that goes with them, which will exceed the £18m cost-only figure. This is the joint confidence level in Hulett's terminology.
Tests that the model is genuinely integrated
Time-related costs are formulas on simulated duration. Test it: lengthen one critical activity and check that preliminaries, staff and plant move. If they do not, the model gives integrated-looking outputs but is two separate analyses.
Each risk has one occurrence draw per iteration, shared by its cost and schedule effects. A risk that delays an activity and creates rework cost must not be sampled twice.
The cost impact of a risk is tied to its schedule impact where one causes the other, such as prolongation on the delayed activity or rework on successors.
Dependencies between drivers are stated, each with a reason, and tested for sensitivity.
The cost model sits on schedule logic. A cost-only model with a single duration input cannot see which path controls the finish, or merge bias: where parallel paths converge, the finish tends to be later than the longest single-path estimate suggests, because any path may turn out longest. The direction and size of the cost error depend on the model, so test it rather than assume.
Drivers exist only where the cause and the affected activities are understood and written down.
The report states the drivers, the dependency structure, the time-related cost rates, the iteration count and the seed check.
When integration is worth building
Compare the cost of a plausible delay with the contingency. In the example, P80 is 16 weeks over baseline (120 less 104), so time-related cost is 16 x £0.5m = £8.0m. Against £18m of contingency that is 44%, which is too large to leave outside the model. If the same calculation gives a small fraction, separate analyses with a stated allowance, or an EMV approach, may be enough.
Integration is strongest on long programmes with fixed external milestones, a fixed budget, material time-related cost and a board that is asking about both together. Check the quality of the schedule before scoping the build, because a poor schedule is where most of the effort goes.
Briefing the client on the result
Boards do not read joint distributions easily. Report three things: the marginal cost S-curve, the marginal schedule S-curve, and a table like the one above that gives cost for each date percentile. Define the metric in a footnote, because 'cost at the P80 date' can mean several things.
The recommendation follows the client's posture. Managing to a date: size contingency to the cost at that date percentile. Managing to a cost ceiling: size it to the cost percentile and accept the schedule exposure. Setting both: quote the joint confidence, and expect to fund above the separate P80s.
The confidence level is the sponsor's choice. The HM Treasury Green Book (2026 edition) requires optimism-bias and risk adjustment but does not set P80 as the funding confidence. Funding levels come from the sponsor, delivery body or approving authority, including NISTA (formerly the IPA) guidance where the project falls under it. Ask for the written rule. Some private clients use P50 for central estimates and P90 for funding ceilings, and portfolio owners may fund contingency centrally at a lower confidence per project. Present the integrated result clearly and let the client choose with the joint exposure in view.
How SOMA approaches this
On a QCRA or QSRA we check first whether time-related cost responds to simulated duration, and we agree the joint-confidence question with the client before building. National Highways QRA is organised as separate QSRA and QCRA reports. Where a client wants a joint view, we state the dependency assumptions and the metric definitions alongside the numbers.