ModelRisk example · General techniques
Cascading Risks
How much do the links between risks add to the contingency? Ten project risks, some of which trigger others.
From the model’s saved run
Risk contingency without and with the links
The total cost of the risks at the confidence level on the Inputs sheet, from the same draws both ways.
| Measure | Unit | Value |
|---|---|---|
| Expected cost of the register, risks independent | US$m | 18.6 |
| Mean total, risks independent (simulated) | US$m | 18.8 |
| Mean total, with the links (simulated) | US$m | 21.5 |
| Contingency, risks independent | US$m | 29.8 |
| Contingency, with the links | US$m | 35.2 |
| Contingency the links add | US$m | 5.4 |
| Confidence level (Inputs sheet) | 80% |
S-curve (cumulative probability) of Risks independent, With the links from the saved simulation.
The business question
A plant upgrade has ten risks on its register, each with a probability and a cost range. Registers usually treat their risks as independent, but some of these are linked. If the regulator approves the design late (A) or the ground turns out worse than surveyed (C), the foundations are much more likely to need a redesign (D): 50% instead of 15%.
A late approval or a redesign makes it more likely that the programme has to be accelerated with overtime and extra shifts (E): 45% instead of 22%.
And if the specialist contractor is unavailable, the ground is bad, the programme is accelerated and prices rise, all in the same project (B, C, E and F), a major claim from the main contractor (H) becomes more likely (13% instead of 5%) and 3.2 times as large.
The model simulates the register twice from the same draws, once as if the risks were independent and once with the links, so the difference between the two totals is the effect of the links alone.
- Who it is for
- Risk analysts, project managers and anyone who keeps a risk register and suspects that its risks are not independent.
- Main outputs
- The total cost of the risks with and without the links, from the same draws · the contingency at the chosen confidence level both ways and the difference · how much more likely the linked risks become · the risks that drive the total.
How the model works
Three sheets after this one, read from left to right. Each one feeds the next.
Inputs sheet
The rules that link the risks: the probability of D, E and H when the risks that trigger them happen, and the factor on H's impact. And the confidence level at which the contingency is read.
Risks sheet
The register gives each risk its probability on its own and a three-point cost range. In every iteration each risk gets two draws: a chance draw that decides whether it happens and a how-bad draw that places its cost in the range.
With the links, D, E and H first look at whether the risks that trigger them happened, and use the raised probability if they did. Both versions of the register use the same draws: a higher probability only adds iterations in which the risk happens, so the difference between the two totals is the effect of the links.
Results sheet
The contingency at the chosen confidence level without and with the links, the S-curves of both totals, how much more likely D, E and H become, and the risks that drive the total.
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The results in detail
Cost ranges
P50 / P80 / P90: a 50%, 80% and 90% chance of not being exceeded.
| Measure | Unit | P50 | P80 | P90 | Mean |
|---|---|---|---|---|---|
| Total, risks independent | US$m | 16.9 | 29.8 | 37.5 | 18.8 |
| Total, with the links | US$m | 20.1 | 35.2 | 44.0 | 21.5 |
| Added by the links | US$m | 0.0 | 0.0 | 13.4 | 2.7 |
| Measure | Unit | Value |
|---|---|---|
| Chance that the links add cost | probability | 19.6% |
How the links change the linked risks
How often each linked risk happens: on its own, and in the simulation with the links.
| Linked risk | On its own | With the links | Change |
|---|---|---|---|
| D Foundations redesigned | 15.0% | 28.3% | 13.3% |
| E Programme accelerated | 22.0% | 31.9% | 9.9% |
| H Major claim | 5.0% | 5.2% | 0.2% |
| H's cost multiplied (B, C, E and F all happen) | 0.0% | 0.07% | 0.07% |
Which risks matter
Lowest and highest mean total with the links over ten equal groups of each risk's cost (VoseSimSensitivityMean).
Tornado chart: the inputs ranked by how far the mean output moves across each input’s range.
The ranking as a table 10 inputs
| Input (ranked by influence) | Lowest mean | Highest mean | Rank |
|---|---|---|---|
| D Foundations must be redesigned | 15.5 | 38.7 | 1 |
| C Ground conditions worse than the survey showed | 19.6 | 38.8 | 2 |
| A Regulator approves the design late | 16.5 | 35.1 | 3 |
| J Key equipment delivered late | 18.1 | 34.0 | 4 |
| B Specialist contractor not available when needed | 19.0 | 34.6 | 5 |
| E Programme must be accelerated | 17.3 | 31.6 | 6 |
| I Commissioning tests fail and must be repeated | 19.3 | 32.6 | 7 |
| H Main contractor files a major claim | 20.9 | 33.4 | 8 |
| G Severe weather stops site work | 20.9 | 29.7 | 9 |
| F Steel and cable prices rise | 20.7 | 27.4 | 10 |
How to read these results
- Both totals come from the same draws. A link only raises a probability, so with the links a risk happens in every iteration in which it happened on its own, and in some more: the difference between the totals is the effect of the links alone, not sampling noise.
- The links add more to the contingency than to the mean: they make risks happen together, so bad outcomes cluster. A contingency set as if the risks were independent is then exceeded more often than its confidence level says: with the inputs as shipped, the independent P80 is exceeded about three times in ten, not two.
- D and E become much more likely because their triggers are common: A happens three times in ten. The rule for H looks dramatic but needs four risks at once, so it applies in very few iterations and adds little to any statistic.
- The tornado ranks the risks by their effect on the total with the links. C happens only one time in ten, yet ranks second: when it happens, D becomes much more likely, and through D so does E. A ranks above risks with larger costs for the same reason.
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.
The links between the risks 4 inputs
What happens to D, E and H when the risks that trigger them happen. Each risk's probability on its own and its cost range are on the Risks sheet.
| Assumption | Unit | Value |
|---|---|---|
| D Foundations redesigned: probability if A or C happensOn its own: 15%. A late approval or bad ground often forces a redesign. | probability | 50% |
| E Programme accelerated: probability if A or D happensOn its own: 22%. A late approval or a redesign leaves less time. | probability | 45% |
| H Major claim: probability if B, C, E and F all happenOn its own: 5%. A contractor hit by all four has grounds for a claim. | probability | 13% |
| H Major claim: cost factor if B, C, E and F all happenThe claim's whole cost range is multiplied by this factor. | × | 3.2 |
Contingency policy 1 input
The confidence level at which the contingency is read.
| Assumption | Unit | Value |
|---|---|---|
| Confidence level for the contingencyP80 is a common choice for a project's risk contingency. | probability | 80% |
Units and conventions
- Money
- US$ million (US$m).
- On its own
- A risk's probability when nothing is known about the other risks: the register's usual number.
- With the links
- The probability, or impact, once it is known which of the risks that trigger it have happened.
- Draws
- Each risk's chance draw and how-bad draw are uniform numbers between 0 and 1, shared by both versions of the register.
Key assumptions and limitations
- Links
- Only the three links on the Inputs sheet are modelled: every other pair of risks is independent.
- Order
- A risk is only triggered by risks above it in the list, so the links are worked out from top to bottom.
- Impacts
- Each cost range is a PERT distribution from 80% to 150% of its most likely value.
- Data
- The project and its risks are invented for this example. The probabilities, cost ranges and links are those of ModelRisk's earlier Cascading Risks example.
How to use it
- Replace the ten risks on the Risks sheet with your own: probability and cost range.
- Change the links in the 'Triggered?' column on the Risks sheet (an OR or an AND of the risks that raise it), and the raised probabilities and the impact factor on the Inputs sheet. A risk can only be triggered by risks above it.
- Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set).
- Compare the contingency without and with the links: if they differ a lot, the links belong in the register.
The tornado chart fills in after a simulation with ModelRisk’s classic engine.
ModelRisk functions used
- VoseUniform
- The two draws per risk: whether it happens and how bad it is.
- VoseBernoulli
- Whether a risk happens: VoseBernoulli(probability, chance draw). With the same draw, a higher probability makes the risk happen in every iteration it happened in before, and in some more.
- VosePERT
- The cost if the risk happens, placed in its range by the how-bad draw (the U argument).
- VoseInput, VoseOutput
- Name each risk's cost with the links and the totals, for the Results Viewer and the sensitivity analysis.
- VoseSimMean, VoseSimPercentile
- Statistics of the simulation for the tables and charts on the Results sheet.
- VoseSimSensitivityMean
- The tornado chart: each risk ranked by how far the mean total moves across the range of its cost.
Further reading
- How to calculate cost contingency (Vose guide)
- Sensitivity analysis in Excel: a tornado chart step by step (Vose guide)
- Vose, D. (2008). Risk Analysis: A Quantitative Guide, 3rd edition. Wiley: modelling correlation and dependencies with logic in the model.
- Hillson, D. and Simon, P. (2020). Practical Project Risk Management: The ATOM Methodology, 3rd edition. Berrett-Koehler.
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.