Vose SoftwareModelRisk example · Projects and construction
Schedule Risk on a Project Network
When will the new bridge open? Schedule risk on the activity network: completion date, criticality and merge bias.
From the model’s saved run
Completion
Weeks from the start. The contract allows the duration on the Inputs sheet.
S-curve (cumulative probability) of Completion from the saved simulation.
| Measure | Unit | Value |
|---|---|---|
| Contract duration (Inputs sheet) | weeks | 44 |
| Contract completion date | date | 3 Jan 2028 |
| Chance of finishing within the contract | probability | 57.9% |
| P80 completion | weeks | 45.6 |
| P80 completion date | date | 14 Jan 2028 |
| Mean completion (simulated) | weeks | 43.6 |
| Deterministic completion, most likely durations | weeks | 40.0 |
| Deterministic completion, mean durations | weeks | 42.7 |
| Effect of skewed durations (mean − most likely schedule) | weeks | 2.7 |
| Merge bias (simulated mean − mean-duration schedule) | weeks | 1.0 |
The business question
A council is replacing an old road bridge. The programme has fifteen activities: design, demolition, piling and walls for two abutments, a pier in the river, girders fabricated off site, then the deck, surfacing and opening. With most likely durations the critical path gives 40 weeks, and the contract allows 44.
But durations are uncertain and skewed — things are more likely to take longer than shorter — and four paths must all be finished before the girders can be erected. Wherever parallel paths join, the later of them sets the pace, so the project is late if any one of them is. That 'merge bias' is invisible in a deterministic programme.
The model draws every duration, schedules the network forwards and backwards in every iteration, and reports the completion date, the chance of meeting the contract, and how often each activity is critical.
- Who it is for
- Planners, project managers and contractors who prepare or review programmes.
- Main outputs
- Completion in weeks and as a date: P50 / P80 / P90 · chance of meeting the contract date · the effect of skewed durations and of merge bias · each activity's criticality index and its influence on the finish · a Gantt chart of each iteration.
How the model works
Three sheets after this one, read from left to right. Each one feeds the next.
Inputs sheet
The start date, the contract duration, and a risk event: a flood that stops work on the river pier.
Network sheet
Each activity has a PERT duration and finish-to-start predecessors. Each start is the latest finish of its predecessors (forward pass). Each latest finish is the earliest latest-start of its successors (backward pass). Float is the difference; an activity with no float is critical in that iteration. The same network is also scheduled with most likely and with mean durations, for comparison.
Results sheet
Completion percentiles and dates, the chance of finishing within the contract, the gap between the deterministic and the simulated finish split into skew and merge bias, and for each activity how often it is critical and how strongly its duration drives the finish.
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The results in detail
Completion percentiles
P50 / P80 / P90: a 50%, 80% and 90% chance of finishing by then.
| Measure | Unit | P50 | P80 | P90 | Mean |
|---|---|---|---|---|---|
| Completion | weeks | 43.5 | 45.6 | 46.7 | 43.6 |
Which activities are critical
Criticality index: how often the activity is on the critical path in the simulation.
| Activity | Critical, most likely | Criticality index |
|---|---|---|
| A Design and approvals | yes | 100% |
| B Site set-up and traffic management | yes | 99% |
| C Demolish the old bridge | yes | 99% |
| D North abutment piling | yes | 37% |
| E South abutment piling | yes | 43% |
| F River pier | 19% | |
| G Fabricate steel girders (off site) | 1% | |
| H North abutment walls | yes | 37% |
| I South abutment walls | yes | 43% |
| J Deliver and erect girders | yes | 100% |
| K Deck slab | yes | 100% |
| L Waterproofing and surfacing | yes | 92% |
| M Parapets and finishes | 8% | |
| N Approach road tie-ins | 0% | |
| O Testing and opening | yes | 100% |
Which durations drive completion
Lowest and highest mean completion 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 16 inputs
| Input (ranked by influence) | Lowest mean | Highest mean | Rank |
|---|---|---|---|
| A Design and approvals | 41.5 | 46.4 | 1 |
| K Deck slab | 42.6 | 45.0 | 2 |
| C Demolish the old bridge | 42.6 | 44.9 | 3 |
| E South abutment piling | 43.0 | 45.3 | 4 |
| F River pier | 43.3 | 45.5 | 5 |
| J Deliver and erect girders | 42.8 | 44.8 | 6 |
| B Site set-up and traffic management | 42.8 | 44.6 | 7 |
| L Waterproofing and surfacing | 42.9 | 44.7 | 8 |
| D North abutment piling | 43.2 | 44.7 | 9 |
| Flood delay | 43.4 | 44.8 | 10 |
| H North abutment walls | 43.3 | 44.1 | 11 |
| I South abutment walls | 43.3 | 44.1 | 12 |
| O Testing and opening | 43.4 | 43.9 | 13 |
| G Fabricate steel girders (off site) | 43.5 | 43.9 | 14 |
| N Approach road tie-ins | 43.5 | 43.8 | 15 |
| M Parapets and finishes | 43.5 | 43.8 | 16 |
How to read these results
- The deterministic programme finishes in 40 weeks, but that date is rarely met: most likely durations add up to less than the median, and wherever paths join, the latest of them sets the pace (merge bias). The two effects are shown separately.
- Activities that are critical in the deterministic programme are not always critical in practice, and others become critical when they overrun: the criticality index measures how often each one controls the finish.
- Effort to recover the schedule pays off on activities with a high criticality index and a strong influence: shortening a non-critical activity changes nothing.
- Common causes such as productivity or weather can make durations move together, which widens the range; this model treats them as independent.
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.
Programme 2 inputs
When the work starts and what the contract allows.
| Assumption | Unit | Value |
|---|---|---|
| Start dateNotice to proceed (1 March 2027). | date | 1 Mar 2027 |
| Contract durationCompletion date in the contract: 44 weeks after the start. | weeks | 44 |
Risk event 2 inputs
A flood stops work in the river until the water level drops.
| Assumption | Unit | Uncertainty | Low | Most likely | High |
|---|---|---|---|---|---|
| Chance of a flood during the pier worksGauge records: one flood in four winters over the cofferdam's design level. | probability | Fixed | 25% | ||
| Delay to the river pier from a floodPumping out, inspection and repair of the cofferdam. | weeks | Risk event · PERT | 2.0 | 3.0 | 6.0 |
Units and conventions
- Time
- Weeks from the start of the project; dates are the start date plus whole weeks.
- Critical
- An activity is critical in an iteration if it has no float: any delay to it delays the opening.
- Criticality index
- The share of iterations in which an activity is critical.
- P50 / P80 / P90
- A 50%, 80% and 90% chance of finishing by then.
Key assumptions and limitations
- Logic
- Finish-to-start links only, no lags; resources are not limited; no weather calendar apart from the flood risk.
- Independence
- Durations are independent of each other; in practice common causes (productivity, weather) can link them.
- Flood
- A flood adds its delay to the river pier only.
- Data
- The project and all durations are invented for this example.
How to use it
- Enter your activities' three-point durations on the Network sheet. The logic (predecessors) is built into the Start formulas: each takes the latest finish of the activities listed.
- Set the start date, the contract duration and the risk event on the Inputs sheet.
- Press F9 to watch the Gantt chart change, then run a simulation from the ModelRisk ribbon (10,000 samples).
- Focus schedule recovery on activities with a high criticality index and a strong influence on the finish.
The tornado chart fills in after a simulation with ModelRisk’s classic engine.
ModelRisk functions used
- VosePERT
- Each activity's duration from its low, most likely and high estimates.
- VoseRiskEvent, VosePERTObject
- The flood: no delay, or a PERT number of weeks.
- VoseInput, VoseOutput
- Name the durations and the outputs, including whether each activity is critical.
- VoseSimMean, VoseSimPercentile
- Statistics of the simulation for the tables and charts on the Results sheet.
- VoseSimSensitivityMean
- The tornado chart: every VoseInput ranked by how far the mean completion moves across its range.
Further reading
- Sensitivity analysis in Excel: a tornado chart step by step (Vose guide)
- Hulett, D. T. (2009). Practical Schedule Risk Analysis. Gower.
- MacCrimmon, K. R. and Ryavec, C. A. (1964). An analytical study of the PERT assumptions. Operations Research 12(1), 16–37.
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.