Vose SoftwareModelRisk example · Projects and construction
Integrated Cost and Schedule Risk
Budget and completion date together: how confident can the sponsor be of both, for the treatment works upgrade?
From the model’s saved run
Cost and completion
The deterministic plan against the simulation.
| Measure | Unit | Value |
|---|---|---|
| Deterministic cost (most likely, no risk) | US$m | 26.70 |
| Mean cost (simulated) | US$m | 28.15 |
| Deterministic completion | weeks | 62.0 |
| Mean completion (simulated) | weeks | 67.0 |
| Rank correlation between cost and completion | 0.81 |
| Measure | Unit | P50 | P70 | P80 | Mean |
|---|---|---|---|---|---|
| Total cost | US$m | 28.07 | 28.74 | 29.16 | 28.15 |
| Completion | weeks | 66.7 | 69.5 | 71.4 | 67.0 |
S-curve (cumulative probability) of Total cost from the saved simulation.
The business question
A water company is upgrading a wastewater treatment works: new tanks, new process equipment, and the old works decommissioned. The deterministic plan says US$26.7 million and 62 weeks. Two things make that plan optimistic. First, much of the cost depends on time: crews, plant and site management are paid by the week, so a longer project costs more — cost and schedule are linked.
Second, durations do not vary independently: site productivity affects every site activity at once. The model schedules the network in every iteration, prices each activity's time-dependent and fixed cost, adds risk events that bring both delay and cost, and records whether the project meets the budget, the deadline and both.
The joint confidence level (JCL) — the chance of meeting both — is what a sponsor approving a budget and a date together really needs, and it is lower than either confidence on its own.
- Who it is for
- Project directors, project controls and cost engineers, sponsors and boards approving budgets and dates together.
- Main outputs
- Cost and completion: P50 / P70 / P80 · the correlation between them · the chance of meeting the budget, the deadline and both (joint confidence level, JCL) at the targets · a JCL table for budgets and deadlines around the targets · the drivers.
How the model works
Three sheets after this one, read from left to right. Each one feeds the next.
Inputs sheet
The budget and deadline to test, the site productivity factor (Lognormal around 1, applied to every site activity), the weekly site overheads, and three risk events. Ground conditions and commissioning problems bring both delay and cost, drawn from one shared uniform so that a bad case is bad in both.
Plan sheet
Each activity has a PERT duration (× productivity for site work, + any risk delay), a time-dependent rate and a PERT fixed cost (+ any risk cost). A small risk table holds this iteration's risk delays and costs, and each activity picks up its own with SUMIF.
Starts follow the network; activity cost = fixed cost + risk cost + rate × duration; the project adds overheads × finish.
Results sheet
Percentiles of cost and finish, their correlation, the chance of meeting the budget, the deadline and both (VoseSimJointProb), the chance of meeting both P80s, the JCL table, and what drives the cost.
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The results in detail
Joint confidence at the targets
Budget and deadline from the Inputs sheet. VoseSimJointProb: the share of iterations that meet both.
S-curve (cumulative probability) of Completion from the saved simulation.
| Measure | Unit | Value |
|---|---|---|
| Budget · deadline | 29.5 US$m · 70 weeks | |
| Chance of meeting the budget | probability | 86.0% |
| Chance of meeting the deadline | probability | 72.8% |
| Chance of meeting both (joint confidence level) | probability | 71.1% |
| If cost and time were independent (budget × deadline) | probability | 62.6% |
A P80 budget and a P80 date are not an 80% plan
Each is met with an 80% chance on its own; both together less often.
| Measure | Unit | Value |
|---|---|---|
| P80 cost | US$m | 29.16 |
| P80 completion | weeks | 71.4 |
| Chance of meeting both the P80 cost and the P80 date | probability | 73.6% |
Joint confidence level table
Chance of meeting both, for budgets (rows) and deadlines (columns) around the targets: VoseSimJointProb for each pair.
| Budget (US$m) | 64 | 67 | 70 | 73 | 76 |
|---|---|---|---|---|---|
| 27.5 | 22% | 29% | 31% | 31% | 31% |
| 28.5 | 29% | 47% | 59% | 62% | 63% |
| 29.5 | 30% | 52% | 71% | 82% | 85% |
| 30.5 | 30% | 52% | 73% | 87% | 94% |
| 31.5 | 30% | 52% | 73% | 87% | 95% |
The centre cell is the target pair. Green: a high chance of meeting both; red: low. The steps between rows and columns are on the Inputs sheet.
What drives the cost
Lowest and highest mean total cost over ten equal groups of each input (VoseSimSensitivityMean), drawn from the overall mean.
Tornado chart: the inputs ranked by how far the mean output moves across each input’s range.
The ranking as a table 13 inputs
| Input (ranked by influence) | Lowest mean | Highest mean | Rank |
|---|---|---|---|
| Site productivity factor | 26.99 | 29.39 | 1 |
| Duration: concrete tanks | 27.07 | 29.31 | 2 |
| Duration: excavation and piling | 27.20 | 29.18 | 3 |
| Duration: mechanical installation | 27.18 | 29.15 | 4 |
| Ground risk (delay and cost) | 27.64 | 29.45 | 5 |
| Duration: electrical installation | 27.33 | 28.97 | 6 |
| Duration: commissioning | 27.39 | 28.87 | 7 |
| Duration: enabling works | 27.42 | 28.86 | 8 |
| Duration: old works and landscaping | 27.46 | 28.88 | 9 |
| Fixed cost: process equipment | 27.60 | 28.74 | 10 |
| Commissioning risk (delay and cost) | 27.94 | 28.98 | 11 |
| Fixed cost: concrete tanks | 27.74 | 28.68 | 12 |
| Fixed cost: excavation and piling | 27.86 | 28.49 | 13 |
How to read these results
- Cost and completion are strongly correlated: weeks cost money, and the same events delay the work and add cost. A late project is an expensive one.
- The chance of meeting both the budget and the deadline is lower than either chance on its own. Approving a P80 budget and a P80 date separately gives about a 74% chance of meeting both, not 80%. The JCL table shows which pairs do reach 80%.
- Because cost and time move together, the joint chance is higher than it would be if they were independent — but it is still limited by the harder of the two targets.
- Site productivity affects every site activity at once, so it drives both the cost and the completion. Durations that move together widen the range compared with independent estimates.
See it move. Open the workbook, change an input on the Inputs sheet and run the simulation: every table and chart on this page updates in Excel.
Inputs and assumptions
Every assumption in the model, with its uncertainty and where it comes from. The figures are illustrative.
Targets 4 inputs
The budget and the completion deadline to test, and the steps between the budgets and deadlines of the JCL table.
| Assumption | Unit | Value |
|---|---|---|
| BudgetProposed budget including contingency. | US$m | 29.5 |
| DeadlineCompletion required by the regulator's permit. | weeks | 70 |
| Step between the budgets in the JCL tableTwo budgets either side of the target. | US$m | 1.0 |
| Step between the deadlines in the JCL tableTwo deadlines either side of the target. | weeks | 3 |
Common factors 2 inputs
Things that affect many activities at once.
| Assumption | Unit | Uncertainty | Low | Most likely | High |
|---|---|---|---|---|---|
| Site productivity factor (× site durations)Labour market and site conditions: 1.10 means every site activity takes 10% longer. | × | Lognormal · P10, P90 | 0.90 | – | 1.10 |
| Site overheadsSite management, welfare, security: paid until completion. | US$k per week | Fixed | 35 | ||
Risk events 8 inputs
The chance of each risk, and its delay and cost if it happens. They are drawn on the Plan sheet; ground conditions and commissioning take their delay and cost from one shared draw.
| Assumption | Unit | Uncertainty | Low | Most likely | High |
|---|---|---|---|---|---|
| Chance of poor ground conditionsBoreholes found soft clay on the east side. | probability | Fixed | 30% | ||
| Ground: delay to excavation and piling, if it happensExtra piling and dewatering. | weeks | PERT · drawn elsewhere | 2.0 | 3.0 | 6.0 |
| Ground: extra cost, if it happensLonger piles, dewatering plant. | US$m | PERT · drawn elsewhere | 0.50 | 0.80 | 1.50 |
| Chance that the process equipment is lateSingle supplier for the membranes, busy order book. | probability | Fixed | 25% | ||
| Equipment: delay, if it is lateDelivery slip. | weeks | PERT · drawn elsewhere | 3.0 | 5.0 | 8.0 |
| Chance of process problems in commissioningBiological process needs time to stabilise. | probability | Fixed | 20% | ||
| Commissioning: delay, if it happensRe-seeding, retesting. | weeks | PERT · drawn elsewhere | 2.0 | 3.0 | 5.0 |
| Commissioning: extra cost, if it happensSpecialists, chemicals, temporary treatment. | US$m | PERT · drawn elsewhere | 0.30 | 0.50 | 0.80 |
Units and conventions
- Money
- US$ million (US$m); rates in US$ thousand per week (US$k/wk).
- Time
- Weeks from the start.
- JCL
- Joint confidence level: the chance that the project meets the budget AND the deadline.
- P50 / P70 / P80
- A 50%, 70% and 80% chance of not being exceeded. Agencies often require a JCL of 70%.
Key assumptions and limitations
- Logic
- Finish-to-start links; no resource limits; overheads run until the last activity finishes.
- Productivity
- One factor scales all site durations together; design and procurement are not affected.
- Risks
- Three risk events; each happens at most once; the delay applies to its activity's duration.
- Data
- The project and all figures are invented for this example.
How to use it
- Review the activities, durations, rates and fixed costs on the Plan sheet, and the risks on the Inputs sheet.
- Set the budget and deadline you want to test on the Inputs sheet.
- Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set).
- Use the JCL table to choose a budget-and-date pair with the confidence the sponsor requires.
- Do not approve the P80 budget and the P80 date as an '80% plan': Results shows how much less likely it is to meet both.
Simulate this model with ModelRisk’s classic engine: it does not run in Turbo mode yet.
ModelRisk functions used
- VosePERT
- Durations and fixed costs from three-point estimates.
- VoseLognormalAlt
- The site productivity factor, from its 10th and 90th percentiles.
- VoseRiskEvent, VosePERTObject, VoseUniform
- Risk events; one shared uniform per risk drives both its delay and its cost.
- VoseInput, VoseOutput
- Name the uncertain quantities and the outputs.
- VoseSimJointProb
- The share of iterations that meet a budget AND a deadline: the joint confidence level.
- VoseSimMean, VoseSimPercentile, VoseSimProbability, VoseSimCorrelation
- Statistics of the simulation for the tables and charts on the Results sheet.
- VoseSimSensitivityMean
- The tornado chart: the thirteen VoseInputs that move the mean total cost most across their range, ranked.
Further reading
- How to calculate cost contingency (Vose guide)
- Sensitivity analysis in Excel: a tornado chart step by step (Vose guide)
- AACE International (2012). Recommended Practice 57R-09: Integrated Cost and Schedule Risk Analysis using Monte Carlo Simulation of a CPM Model.
- NASA (2015). NASA Cost Estimating Handbook, version 4.0 — Joint Cost and Schedule Confidence Level (JCL).
Download the workbook and run it yourself. It opens in Excel with ModelRisk. The free trial runs every example model.
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An illustrative example: the figures are invented for teaching and do not describe a real company, project or asset. Last updated 9 October 2026.