Quantitative Risk Analysis and Modeling Techniques
“Quantitative Risk Analysis and Modeling Techniques” is a tool/technique for the process “Perform Quantitative Risk Analysis “.
Commonly used techniques use both event-oriented and project-oriented analysis approaches, including: – Sensitivity analysis. Sensitivity analysis helps to determine which risks have the most potential impact on the project. It helps to understand how the variations in project?s objectives correlate with variations in different uncertainties. Conversely, it examines the extent to which the uncertainty of each project element affects the objective being studied when all other uncertain elements are held at their baseline values. One typical display of sensitivity analysis is the tornado diagram (Figure 11-15), which is useful for comparing relative importance and impact of variables that have a high degree of uncertainty to those that are more stable. The Tornado diagram is also helpful in analyzing risk-taking scenarios enabled on specific risks whose quantitative analysis highlights possible benefits greater than corresponding identified negative impacts. A tornado diagram is a special type of bar chart used in sensitivity analysis for comparing the relative importance of the variables. In a tornado diagram, the Y-axis contains each type of uncertainty at base values, and the X-axis contains the spread or correlation of the uncertainty to the studied output. In this figure, each uncertainty contains a horizontal bar and is ordered vertically to show uncertainties with a decreasing spread from the base values.
Risk 1 Risk 2 Risk 3 Risk 4 Risk 5 Risk 6 Negative Impact Positive Impact KEY -15,000 -10,000 -5,000 0 5,000 10,000 15,000 20,000
Figure 11-15. Example of Tornado Diagram – Expected monetary value analysis. Expected monetary value (EMV) analysis is a statistical concept that calculates the average outcome when the future includes scenarios that may or may not happen (i.e., analysis under uncertainty). The EMV of opportunities are generally expressed as positive values, while those of threats are expressed as negative values. EMV requires a risk-neutral assumption? neither risk averse nor risk seeking. EMV for a project is calculated by multiplying the value of each possible outcome by its probability of occurrence and adding the products together. A common use of this type of analysis is a decision tree analysis (Figure 11-16).
Computed: Payoffs minus Costs along Path Decision Definition Decision Node Chance Node Net Path Value Decision to be Made Input: Cost of Each Decision Output: Decision Made Input: Scenario Probability, Reward if it Occurs Output: Expected Monetary Value (EMV) Build or Upgrade? $80M 0,6 0,4 0,6 0,4 $36M = .60 ($80M) + -$30M .40 (?$30M) EMV (before costs) of Build New Plant considering demand $46M = .60 ($70M) + .40 ($10M) EMV (before costs) of Upgrade Plant considering demand Decision EMV = $46M (the larger of $36M and $46M) $80M = $200M ? $120M ?$30M = $90M ? $120M $70M = $120M ? $50M $10M = $60M ? $50M $70M $10M Note 1: The decision tree shows how to make a decision between alternative capital strategies (represented as ?decision nodes?) when the environment contains uncertain elements (represented as ?chance nodes?).
Note 2: Here, a decision is being made whether to invest $120M US to build a new plant or to instead invest only $50M US to upgrade the existing plant. For each decision, the demand (which is uncertain, and therefore represents a ?chance node?) must be accounted for. For example, strong demand leads to $200M revenue with the new plant but only $120M US for the upgraded plant, perhaps due to capacity limitations of the upgraded plant. The end of each branch shows the net effect of the payoffs minus costs. For each decision branch, all effects are added (see shaded areas) to determine the overall Expected Monetary Value (EMV) of the decision. Remember to account for the investment costs. From the calculations in the shaded areas, the upgraded plant has a higher EMV of $46M ? also the EMV of the overall decision. (This choice also represents the lowest risk, avoiding the worst case possible outcome of a loss of $30M).
Decision Node Chance Node End of Branch Strong Demand ($200M) Weak Demand ($90M) Strong Demand ($120M) Weak Demand ($60M) Build New Plant (Invest $120M) Upgrade Plant (Invest $50M)
Figure 11-16. Decision Tree Diagram – Modeling and simulation. A project simulation uses a model that translates the specified detailed uncertainties of the project into their potential impact on project objectives. Simulations are typically performed using the Monte Carlo technique. In a simulation, the project model is computed many times (iterated), with the input values (e.g., cost estimates or activity durations) chosen at random for each iteration from the probability distributions of these variables. A histogram (e.g., total cost or completion date) is calculated from the iterations. For a cost risk analysis, a simulation uses cost estimates. For a schedule risk analysis, the schedule network diagram and duration estimates are used. The output from a cost risk simulation using the three-element model and risk ranges is shown in Figure 11-17. It illustrates the respective probability of achieving specific cost targets. Similar curves can be developed for other project objectives.
This cumulative distribution, assuming the data ranges in Figure 11-13 and triangular distributions, shows that the project is only 12 percent likely to meet the $41 million most likely cost estimate. If a conservative organization wants a 75% likelihood of success, a budget of $50 million (a contingency of nearly 22 % ($50M – $41M)/$41M)) is required.
Total Project Cost Cumulative Chart Cost
This definition was found in the PMBOK V5
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