PMGT5891 Chap.7 Quantitative Risk Assessment and Monte Carlo Simulation
Quantitative Risk Assessment and Monte Carlo Simulation
This chapter covers the Weeks 7 to 8 material on quantitative cost risk assessment. You learn to turn a single cost or duration guess into optimistic, most likely and pessimistic values, to compute triangular and PERT means, and to choose between uniform, triangular, Trigen and betaPERT shapes.
It then walks through Monte Carlo simulation in Excel, from random sampling to a cumulative S-curve, and shows how to read P50, P80 and P90 figures as funding advice. Sensitivity analysis with tornado charts, structured scenarios, correlation between inputs and the pooling of expected monetary values complete the toolkit, with every example built on original numbers.
What this chapter covers
- 01
Quantitative cost risk assessment in Excel
- 02
Optimistic, most likely and pessimistic estimates
- 03
Triangular and PERT means, standard deviation and variance
- 04
Uniform, triangular, Trigen and betaPERT distributions
- 05
Monte Carlo steps, iterations and fixed seeds
- 06
Reading P50, P80 and P90 from an S-curve
- 07
Tornado charts and one-way sensitivity
- 08
Scenario analysis and correlated inputs
- 09
Pooling expected monetary values
Worked example · free
PERT expected duration for three sequential tasks
- +1PERT means use (O + 4M + P) / 6. Survey: (4 + 24 + 14) / 6 = 42 / 6 = 7.0 days. Design: (8 + 40 + 18) / 6 = 66 / 6 = 11.0 days. Approvals: (5 + 36 + 25) / 6 = 66 / 6 = 11.0 days.
- +1Expected total = 7.0 + 11.0 + 11.0 = 29.0 days. The most likely values alone add to 6 + 10 + 9 = 25 days, so planning on them understates the sequence by 4 days.
- +1Standard deviations use (P minus O) / 6. Survey: 10 / 6 = 1.67 days. Design: 10 / 6 = 1.67 days. Approvals: 20 / 6 = 3.33 days.
- +1Variances are the squares: 2.78 + 2.78 + 11.11 = 16.67. Because total variance is the sum of task variances, the sequence standard deviation is the square root of 16.67, about 4.08 days.
- +1Approvals supplies 11.11 / 16.67 = 67% of the total variance, so it is the task to treat first, for example by lodging the application early and agreeing a pre-lodgement meeting.
Key terms
- Three-point estimate
- A three-point estimate is a forecast given as optimistic, most likely and pessimistic values instead of one figure. It is the input for PERT and for most Monte Carlo models.
- Triangular distribution
- A triangular distribution is a probability shape defined by a minimum, a most likely and a maximum value. Its mean is (Min + Most likely + Max) / 3, and for costs it usually leans to the right.
- Monte Carlo simulation
- Monte Carlo simulation is a method that recalculates a model many times with randomly sampled inputs. The stored results form a distribution of possible totals.
- P80 confidence level
- The P80 confidence level is the value that 80% of simulated outcomes do not exceed. A budget set there leaves about a one-in-five chance of overrun.
- Tornado chart
- A tornado chart is a bar chart that ranks inputs by how strongly each one moves the output. Bars are sorted with the widest at the top, so the chart looks like a tornado.
Quantitative Risk Assessment and Monte Carlo Simulation FAQ
How many iterations does a Monte Carlo cost model need?
Baccarini gives 1,000 to 5,000 as typical, with more needed when a model has many variables or rare events in its tails. The unit's Excel notes add that accuracy improves as calculations increase. When comparing two versions of a model, keep the seed fixed so any difference in results comes from the model change, not from a new random sequence.
When should I use a PERT mean instead of a triangular mean?
Use PERT, (O + 4M + P) / 6, when the most likely value rests on good information and the extremes are shaky; the heavy weight on M keeps an extreme maximum from dragging the mean. Use the triangular mean, (O + M + P) / 3, when you suspect estimators are understating the pessimistic case, since its fatter right tail compensates.
Why does a simulated total usually come out above the sum of most likely costs?
Cost ranges are usually skewed to the right: an item can overrun by far more than it can underrun. Each item's mean therefore sits above its most likely value, and the gaps add up across items. That is why a deterministic base estimate often lands at a low percentile of the simulated S-curve.
What happens if I ignore correlation in a Monte Carlo model?
Independent sampling lets a high draw on one item cancel a low draw on another, so the output range comes out narrower than reality and high percentiles are understated. Positive correlation, such as several items sharing a steel price, widens the spread. Baccarini cites Chapman and Ward, who hold that a strong-dependence assumption tends to match reality better than independence does.
Exam move
Start by making the three-point formulas automatic: compute a triangular mean, a PERT mean and a PERT standard deviation for five invented items until each takes under a minute. Then open the unit's Monte Carlo template, change one item's maximum, and watch how P50 and P80 move; write one sentence each time explaining what the shift means for a sponsor.
Practise reading a cumulative table: given a percentile list and a base estimate, state the contingency for P50, P80 and P90 and the share of runs that overrun the base. Build a small tornado by hand for a four-item estimate so you can explain why the top bar deserves treatment first.
Finally, rehearse two short critiques you can use in any answer: false precision from extensive calculation, and narrow results when correlation is ignored. Keep every calculation laid out step by step so the reasoning stays visible.
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