Monte Carlo & Latin Hypercube risk analysis
Quantitative cost and schedule risk modeling, contingency curves and joint confidence levels, reported at the confidence levels used in FTA Oversight Procedure 40 (P40, P50, P65, P80).
Every chart on this page comes from a live simulation of a made-up example project (8 cost items, 7 schedule activities, 5,000 trials). It shows our method, not a client result.
From “what if” to a number you can fund
A single-point estimate says the project costs 100. Reality is a range. We model each cost item and schedule activity as a range, run thousands of trials, and report the confidence level the owner chooses to fund.
Input distributions
Illustrative example
What we deliver
- Quantitative and qualitative risk analysis and risk register
- Cost contingency curve with minimum contingency levels
- Beta Range Factor assessment, forward pass and backward pass
- Contingency drawdown and risk trend analysis reports
- Design, market and construction risk, and adequacy of budget and schedule
- SCC cost workbook conditioning
Monte Carlo simulation
Each trial draws a random value for every uncertain item and adds them up. Thousands of trials build the distribution of total cost.
Cost outcome distribution
Illustrative example
What drives the total?
Illustrative example
Latin Hypercube sampling
Latin Hypercube divides each input into equal-probability slices and uses every slice exactly once. Samples cover the whole range evenly, so you need fewer trials for the same accuracy.
Random vs. stratified sampling
Monte Carlo vs. Latin Hypercube
Same model, same inputs. We measure how close each method gets to a 100,000-trial reference answer.
Cumulative distribution (S-curve)
Illustrative example
Convergence of the P80 estimate
Illustrative example
Contingency and FTA Oversight Procedure 40C
We report results at P40, P50, P65 and P80, show the cumulative S-curve and cost-risk probability graphs, and build contingency curves and drawdown tracking. FTA has used P65 for cost contingency since July 2018.
Cost contingency curve
Illustrative example
Minimum contingency drawdown
Illustrative example
What OP 40C asks for, and how we deliver it
| OP 40C element | What Vanguard Resolve delivers |
|---|---|
| Stripped and adjusted baseline (schedule and cost) | We remove both exposed and hidden contingency from the baseline estimate and schedule, then adjust for our findings, so the model starts from a clean base. |
| Risk workshops | We facilitate and document workshops with the sponsor and oversight team to confirm scope, cost, schedule and the risk register. |
| Beta Range Factors | We use Beta Range Factors to benchmark uncertainty and adjust them for project-specific conditions. |
| Cost and schedule risk models | Top-down cost risk and a stochastic CPM schedule model, run with Monte Carlo and Latin Hypercube sampling. |
| Confidence levels | Results at P40, P50, P65 and P80. FTA has used P65 for cost contingency since July 2018. |
| Schedule contingency | Reported against the remaining critical path, generally 125% of its duration or the P65 histogram result, whichever is larger. |
| Allocated and unallocated contingency | We separate contingency embedded in activities from contingency held as placeholders, and track both. |
| Contingency curves and drawdown | Minimum-contingency curves by project phase, with drawdown tracked against them. |
| Mitigation | Avoidance, transfer, reduction and acceptance, with secondary mitigation characterized where identified. |
| Reporting graphics | Histogram with cumulative S-curve and cost-risk probability graphs, as shown above. |
Vanguard Resolve builds its analysis to follow the elements of FTA Oversight Procedure 40C, Risk and Contingency Review (see all FTA oversight procedures). This is not an FTA certification or approval. OP 40 names Monte Carlo as the standard method; we use Latin Hypercube sampling to reach stable results with fewer trials.
Schedule risk and joint confidence
Cost and schedule are linked: a late project costs more. We model them together and report the chance of hitting both targets.
Schedule outcome distribution
Illustrative example
Criticality index
Illustrative example
Joint confidence level (cost and schedule)
Illustrative example