## Quantitative Risk Analysis and Modeling Techniques

Commonly used techniques includc both cvcnt-oricntcd and projcct-oricntcd analysis approaches:

• Sensitivity analysis. Sensitivity analysis helps to determine which risks have the most potential impact on the project. It examines the extent to which the uncertainty of cach project element affects the objective being examined when all other uncertain elements are held at their baseline values. One typical display of sensitivity analysis is the tornado diagram, which is useful for comparing relative importance and impact of variables that have a high degree of uncertainty to those that arc more stable.

• Expected monetary value analysis. Expcctcd 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 wili generally be expressed as positive values, while those of risks wil! be negative. 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 in decision tree analysis (Figure 11 -10).

• Decision tree analysis. Decision tree analysis is usually structured using a decision tree diagram (Figure 11-10) that describes a situation under consideration, and the implications of each of the available choices and possible scenarios. It incorporates the cost of cach available choicc, the probability of cach possible scenario, and the outcomc (net path value) of cach alternative logical path. Solving the decision tree provides the EMV (or other measure of interest to the organization) for each alternative, when all the rewards and subsequent decisions are quantified.

Decision to be Made input: Cost of Each Decision Output: Decision Made

Input: Scenario Probability,

Reward if it Occurs Output: Expected Monetary Value (EMV)

Computed: Payoffs minus Costs along Path

Build New Plant (Invest \$120M)

Build New Plant (Invest \$120M)

EMV (including costs) of Build New Plant

EMV (including costs) of Build New Plant Strong Demand

(Invest \$50M)

EMV (including costs) of Upgrade Plant considering"

Strong Demand

S200M

/ 35%

j S90M

Build New Plant considering

Strong Demand

\$70M

 / 35% Weak Demand <1 S 60 M

\$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").

### Figure 11-10. Decision Tree Diagram

• Modeling and simulation. A projcct simulation uses a mode! that translates the uncertainties specified at a detailed level of the projcct into their potential impact on project objectives. Iterative simulations are typically performed using the Monte Carlo technique. In a simulation, the projcct model is computed many times (iterated), with the input values randomized from a probability distribution function (e.g., cost of project elements or duration of schedule activities) chosen for each iteration from the probability distributions of each variable. A probability distribution (e.g., total cost or completion dale) is calculated from the iterations. For a cost risk analysis, a simulation can use source data from the traditional projcct WBS or a cost breakdown structure. For a schedule risk analysis, the network schedule is used. The output from a cost risk simulation is shown in Figure 11-11. Modeling and simulation are recommended for use in cost and schedule risk analysis, bccausc they arc more powerful and less subject to misuse and/or personal bias than EMV analysis.

Total Project Cost

Cumulative Chart Cost

This cumulative likelihood distribution reflects the risk of overrunning the sum of the most likely cost estimate, assuming the data ranges contained in Figure 11-8 and triangular distributions. It shows that the project is only 12 percent likely to meet the \$41 million estimate, if a conservative organization wants a 75% likelihood of success, a budget of \$50 million {a contingency of nearly 22 %) is required.

Cost

This cumulative likelihood distribution reflects the risk of overrunning the sum of the most likely cost estimate, assuming the data ranges contained in Figure 11-8 and triangular distributions. It shows that the project is only 12 percent likely to meet the \$41 million estimate, if a conservative organization wants a 75% likelihood of success, a budget of \$50 million {a contingency of nearly 22 %) is required.

### Figure 11-11. Cost Risk Simulation Results

Models arc not exclusively iterative. They may also include basic mathematical derivations. The Program Evaluation and Review Technique (PERT) is a more rudimentary approach to quantitative analysis. (PERT applies a weighted average favoring the most likely outcome.):

While such non-iterative models do not take merge bias into account (as Monte Carlo docs), they do provide alternative (and more optimistic) approaches for calculating the relative risk of a project. 