ModelRisk example · General techniques
Correlation Through a Common Factor (Look-up Table)
How much later does a project finish when bad weather hits every activity at once? Correlation through a common factor.
From the model’s saved run
Total time three ways
The same base durations with no weather effect, with the season shared by every activity, and with independent weather for each.
| Measure | Unit | 10th pct | Median | 90th pct | Mean |
|---|---|---|---|---|---|
| No weather effect | weeks | 47.6 | 50.0 | 52.5 | 50.0 |
| Shared weather | weeks | 46.5 | 51.4 | 60.3 | 52.7 |
| Independent weather | weeks | 48.8 | 52.6 | 56.8 | 52.7 |
| Measure | Unit | Value |
|---|---|---|
| Standard deviation, shared weather | weeks | 5.36 |
| Standard deviation, independent weather | weeks | 3.10 |
| Standard deviation, no weather effect | weeks | 1.88 |
S-curve (cumulative probability) of Shared weather, Independent weather, No weather effect, Deadline from the saved simulation.
The business question
A contractor schedules six activities one after the other: archaeology, digging the foundations, formwork, laying the foundations, walls and floors, and the roofing. Each has a three-point estimate for normal weather.
The season's weather is graded from 1 (very poor) to 5 (very good), and a table says how much each activity's duration changes with it: in very poor weather laying the foundations takes 40% longer, in very good weather 18% less. All six activities face the same season, so the weather makes them late or early together.
The model compares three versions from the same base durations: no weather effect, one shared season, and a season of its own for each activity.
- Who it is for
- Anyone who has to correlate many variables that depend on one outside influence: weather, the economy, a market, an exchange rate.
- Main outputs
- Total time at P10 / median / P90 with no weather effect, with one shared season, and with independent weather for each activity · the chance of missing the deadline both ways · the correlation the shared weather creates · the drivers.
How the model works
Three sheets after this one, read from left to right. Each one feeds the next.
Inputs sheet
Each activity's duration in normal weather as a triangular distribution, and the deadline.
Activities sheet
The weather table gives each activity's change in duration for each grade. With shared weather, one draw of the weather index picks the column for every activity (INDEX). With independent weather each activity draws its own index. Both versions use the same base durations.
Results sheet
The total time in the three versions, the chance of missing the deadline with shared and with independent weather, the correlation between two activities, and the tornado.
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The results in detail
What sharing the weather does
The deadline is on the Inputs sheet.
| Measure | Unit | Value |
|---|---|---|
| Chance of missing the deadline, shared weather | probability | 36.7% |
| Chance of missing the deadline, independent weather | probability | 23.0% |
| Rank correlation, digging and laying foundations: shared | 0.79 | |
| Rank correlation, digging and laying foundations: independent | 0.01 |
What moves the total
Lowest and highest mean total with shared weather over ten equal groups of each input (VoseSimSensitivityMean).
Tornado chart: the inputs ranked by how far the mean output moves across each input’s range.
The ranking as a table 7 inputs
| Input (ranked by influence) | Lowest mean | Highest mean | Rank |
|---|---|---|---|
| Weather index this season | 46.6 | 61.5 | 1 |
| Walls and floors | 50.6 | 55.0 | 2 |
| Dig foundations | 51.2 | 54.4 | 3 |
| Archaeology | 51.7 | 54.5 | 4 |
| Lay foundations | 51.7 | 54.1 | 5 |
| Lay roofing | 51.9 | 54.1 | 6 |
| Formwork | 52.3 | 53.4 | 7 |
How to read these results
- The weather adds about 2.7 weeks on average in both weather versions: sharing the season does not change the mean.
- It changes the spread. With one season for the whole job, the standard deviation is about 5.3 weeks against 3.1 with independent weather, and the 90th percentile about 60 weeks against 57: a bad season slows every activity at once, while independent weather averages out.
- So the chance of missing the 55-week deadline is about 37% with shared weather, and only about 23% if the correlation were ignored.
- The look-up table correlates the activities without a correlation coefficient: digging and laying the foundations move together (rank correlation about 0.8) because they read the same column of the table. The tornado puts the weather first.
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.
Base durations 6 inputs
Each activity's duration in normal weather (weeks).
| Assumption | Unit | Uncertainty | Low | Most likely | High |
|---|---|---|---|---|---|
| ArchaeologyLow, most likely and high, as in the original example. | weeks | Triangle | 3.0 | 4.0 | 6.0 |
| Dig foundations | weeks | Triangle | 9.0 | 11.0 | 13.0 |
| Formwork | weeks | Triangle | 2.0 | 2.0 | 3.0 |
| Lay foundations | weeks | Triangle | 6.0 | 7.0 | 9.0 |
| Walls and floors | weeks | Triangle | 15.0 | 17.0 | 21.0 |
| Lay roofing | weeks | Triangle | 6.0 | 7.0 | 9.0 |
Deadline 1 input
| Assumption | Unit | Value |
|---|---|---|
| Deadline for the six activitiesAbout five weeks more than with no weather effect. | weeks | 55 |
Units and conventions
- Time
- Weeks.
- Weather index
- 1 very poor, 2 poor, 3 normal, 4 good, 5 very good.
- Change
- The percentage added to (or taken off) an activity's normal-weather duration.
Key assumptions and limitations
- In sequence
- The six activities run one after the other; the total is their sum.
- One season
- With shared weather, the whole job sees one season's weather; the independent version is for comparison only.
- Data
- The activities, durations, weather table and weather weights are those of ModelRisk's earlier Correlation Using Look-up Tables example.
How to use it
- Change the base durations and the deadline on the Inputs sheet.
- Change the weather's chances and its table on the Activities sheet: one row per activity, one column per grade.
- Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set).
- Compare the shared and the independent versions: the difference is what ignoring the correlation would hide.
The tornado chart fills in after a simulation with ModelRisk’s classic engine.
ModelRisk functions used
- VoseTriangle
- Each activity's duration in normal weather.
- VoseDiscrete
- The weather index: once for the shared season, once per activity for the independent version.
- INDEX (Excel)
- The look-up: the change in duration for this weather grade, from the activity's row of the table.
- VoseInput, VoseOutput
- Name the base durations, the weather and the three totals.
- VoseSimCorrelation
- The rank correlation the shared weather creates between two activities.
- VoseSimMean, VoseSimStdev, VoseSimPercentile
- Statistics of the simulation.
- VoseSimSensitivityMean
- The tornado chart: what moves the mean total with shared weather.
Further reading
- 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 through a common factor and look-up tables.
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.